EX-4.2

Exhibit 4.2

FIRST AMENDMENT TO WARRANT TO PURCHASE SHARES OF STOCK

THIS FIRST AMENDMENT TO WARRANT TO PURCHASE SHARES OF STOCK (this “Warrant Amendment”) is entered into as of June 23, 2026, by and between AVENUE VENTURE OPPORTUNITIES FUND II, L.P., a Delaware limited partnership (“Holder”) and CALCIMEDICA, INC., a Delaware corporation (the “Company”).

RECITALS

A. WHEREAS, the Company issued to Holder that certain Warrant to Purchase Shares of Stock dated as of February 28, 2025 (the “Warrant”).

B. WHEREAS, the Company and Holder are parties to those certain Loan Documents dated as of February 28, 2025, including that certain Loan and Security Agreement and Supplement thereto (as amended, restated or supplemented from time to time, the “Agreement” and the “Supplement”, respectively);

C. WHEREAS, the Company and Holder are entering into that certain First Amendment to Loan Documents dated as of even date herewith (the “First Amendment”); and

D. WHEREAS, it is a condition to the First Amendment that the Company executes and delivers this Warrant Amendment in favor of Holder.

NOW, THEREFORE, the parties agree as follows:

1. The definition of “Applicable Number” as set forth on the first page of the Warrant hereby is amended and restated to read as follows:

“Applicable Number” means 641,163 shares of Common Stock purchasable hereunder.

2. The definition of “Stock Purchase Price” as set forth on the first page of the Warrant hereby is amended and restated to read as follows:

“Stock Purchase Price” means $1.00.

3. The following definitions hereby are added to the first page of the Warrant in the appropriate alphabetical order to read as follows:

“Affiliate” means, with respect to any Person, any other Person directly or indirectly controlled by, controlling or under common control with, such Person, but only for so long as such control shall continue. For purposes of this definition, “control” (including, with correlative meanings, “controlled by”, “controlling” and “under common control with”) means, with respect to a Person, possession, direct or indirect, of (i) the power to direct or cause direction of the management and policies of such Person (whether through ownership of securities or partnership or other ownership interests, by contract or otherwise), or (ii) at least 50% of the voting securities (whether directly or pursuant to any option, warrant or other similar arrangement) or other comparable equity interests.

“Attribution Parties” means, collectively, the following Persons and entities: (i) any direct or indirect Affiliates of the Holder, (ii) any Person acting or who could be deemed to be acting as a Group together with the Holder or any Attribution Parties and (iii) any other Persons whose beneficial ownership of the Common Stock would or could be aggregated with the Holder’s and/or any other Attribution Parties for purposes of Section 13(d) or Section 16 of the Exchange Act. For clarity, the purpose of the foregoing is to subject collectively the Holder and all other Attribution Parties to the Maximum Percentage.

“Commission” means the U.S. Securities and Exchange Commission.

“Exchange Act” means the U.S. Securities Exchange Act of 1934, as amended, and all of the rules and regulations promulgated thereunder.

“Group” shall have the meaning ascribed to it in Section 13(d) of the Exchange Act, and all related rules, regulations and jurisprudence.

“Person” and “Persons” means an individual, a limited liability company, a partnership, a joint venture, a corporation, a trust, an unincorporated organization, any other entity and any governmental entity or any department or agency thereof.

“Principal Trading Market” means the principal trading market for the Company’s Common Stock. The “Principal Trading Market” for the Common Stock is the Nasdaq Capital Market.”

New Section 1(c) of the Warrant hereby is added to read as follows:

“(c) Notwithstanding anything to the contrary contained herein, the Company shall not effect the exercise of any portion of this Warrant, and the Holder of the Warrant shall not have the right to exercise any portion of the Warrant, and any such exercise shall be null and void ab initio and treated as if the exercise had not been made, to the extent that immediately prior to or following such exercise, the Holder, together with the Attribution Parties, beneficially owns or would beneficially own as determined in accordance with Section 13(d) of the Exchange Act and the rules promulgated thereunder, in excess of 4.99% (the “Maximum Percentage”) of the Common Stock that would be issued and outstanding following such exercise. For purposes of calculating beneficial ownership for determining whether the Maximum Percentage is or will be exceeded, the aggregate number of shares of Common Stock beneficially owned by the Holder together with the Attribution Parties, shall include the number of shares of Common Stock beneficially owned by the Holder together with the Attribution Parties plus the number of shares of Common Stock issuable upon exercise of the relevant Warrant with respect to which the determination is being made but shall exclude the number of shares of Common Stock which would be issuable upon (i) exercise of the remaining, unexercised portion of this Warrant beneficially owned by the Holder or the Attribution Parties and (ii) exercise or conversion of the unexercised or unconverted portion of any other securities of the Company beneficially owned by such Holder or any Attribution Party (including, without limitation, any convertible notes, convertible stock or warrants) that are subject to a limitation on conversion or exercise analogous to the limitation contained herein. For purposes of this Section 1(c), beneficial ownership of the Holder or the Attribution Parties shall, except as set forth in the immediately preceding sentence, be calculated and determined in accordance with Section 13(d) of the Exchange Act and the rules promulgated thereunder. For purposes of the Warrant, in determining the number of outstanding shares of Common Stock, a Holder of the Warrant may rely on the number of outstanding shares of Common Stock as reflected in (1) the Company’s most recent Annual Report on Form 10-K, Quarterly Report on Form 10-Q, Current Report on Form 8-K or other public filing with the Commission, as the case may be, (2) a more recent public announcement by the Company or (3) any other notice by the Company or the transfer agent setting forth the number of shares of Common Stock outstanding (such issued and outstanding shares, the “Reported Outstanding Share Number”). Upon the written request of the Holder, the Company shall within two (2) business days confirm in writing (including by electronic mail) to the Holder that the number of shares of Common Stock then outstanding is not less than the Reported Outstanding Share Number or, if the number of shares of Common Stock then outstanding is less than the Reported Outstanding Share Number, the Company shall confirm in writing (including by electronic mail) to the Holder the number of shares of Common Stock then outstanding. The Holder shall disclose to the Company the number of shares of Common Stock that it, together with the Attribution Parties beneficially owns and has the right to acquire through the exercise of derivative securities and any limitations on exercise or conversion analogous to the limitation contained herein contemporaneously or immediately prior to submitting the form of subscription for the Warrant. If the Company receives the form of subscription from the Holder at a time when the actual number of outstanding shares of Common Stock is less than the Reported Outstanding Share Number, the Company shall (i) notify the Holder in writing of the

number of shares of Common Stock then outstanding and, to the extent that such form of subscription would otherwise cause the Holder’s, together with the Attribution Parties’, beneficial ownership, as determined pursuant to this Section 1(c), to exceed the Maximum Percentage, the Holder must notify the Company of a reduced number of the shares Common Stock hereunder to be purchased pursuant to such form of subscription (the number of shares by which such purchase is reduced, the “Reduction Shares”) and (ii) as soon as reasonably practicable, the Company shall return to the Holder any exercise price paid by the Holder for the Reduction Shares. In any case, the number of outstanding shares of Common Stock shall be determined after giving effect to the conversion or exercise of securities of the Company, including this Warrant, by the Holder and the Attribution Parties since the date as of which the Reported Outstanding Share Number was reported. In the event that the issuance of Common Stock to the Holder upon exercise of this Warrant results in the Holder, together with the Attribution Parties, being deemed to beneficially own, in the aggregate, more than the Maximum Percentage of the number of outstanding shares of Common Stock (as determined under Section 13(d) of the Exchange Act), the number of shares so issued by which the Holder’s, together with the Attribution Parties’, aggregate beneficial ownership exceeds the Maximum Percentage (the “Excess Shares”) shall be deemed null and void and shall be cancelled ab initio, and the Holder and/or the Attribution Parties shall not have the power to vote or to transfer the Excess Shares. As soon as reasonably practicable after the issuance of the Excess Shares has been deemed null and void, the Company shall return to the Holder the exercise price paid by the Holder for the Excess Shares. By written notice to the Company, a Holder of the Warrant may from time to time increase or decrease the Maximum Percentage to any other percentage not in excess of 19.99% specified in such notice; provided, however, that any increase in the Maximum Percentage will not be effective until the sixty-first (61st) day after such notice is delivered to the Company, any such increase or decrease will apply only to the Holder, and shall not negatively affect any partial exercise effected prior to such change. Notwithstanding anything anywhere in this Warrant to the contrary, the aggregate number of shares issued pursuant to the exercise of this Warrant shall not exceed the aggregate number of shares of Common Stock which the Holder may exercise pursuant to the terms of this Warrant without breaching the Company’s obligations under the rules or regulations of the Principal Trading Market (the number of shares which may be issued without violating such rules and regulations, the “Exchange Cap”), except that such limitation shall not apply in the event that the Company obtains the approval of its stockholders as required by the applicable rules of the Principal Trading Market, including, but not limited to, Nasdaq Rule 5635, for issuances of shares of Common Stock in excess of such amount or such approval is not required pursuant to the applicable rules of the Principal Trading Market.”

Article 10 of the Warrant is hereby amended and restated to read as follows:

“10. Rights and Obligations Survive Exercise of Warrant. The rights and obligations of Company, of Holder of this Warrant and of the holder of shares of Common Stock issued upon exercise of this Warrant, contained in Sections 5, 10, 17 and 18 shall survive the exercise of this Warrant.”

6. This Warrant Amendment shall be affixed to the Warrant and shall become a part thereof for all purposes.

7. Article 14 of the Warrant is incorporated herein by reference, mutatis mutandis, as though set forth in full.

8. Article 19 of the Warrant is incorporated herein by reference, mutatis mutandis, as though set forth in full.

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IN WITNESS WHEREOF, the undersigned has executed this Warrant Amendment as a deed on the day and year first above written.


COMPANY:

CALCIMEDICA, INC.

By:		/s/ Rachel Leheny
Name: Rachel Leheny
Title: Chief Executive Officer


AGREED AND ACCEPTED:

HOLDER:

AVENUE VENTURE OPPORTUNITIES FUND II, L.P.

By: Avenue Venture Opportunities Partners II, LLC
Its: General Partner

By:		/s/ Sonia Gardner
Name: Sonia Gardner
Title: Authorized Signatory

[Signature Page to First Amendment to Warrant to Purchase Shares of Stock]