Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We consent to the incorporation by reference in this Registration Statement on Form S-8 of CalciMedica, Inc., of our report dated March 27, 2025, relating to the consolidated financial statements of CalciMedica, Inc. (the “Company”), appearing in the Annual Report on Form 10-K of the Company for the year ended December 31, 2024, filed with the Securities and Exchange Commission.

/s/ Baker Tilly US, LLP

(formerly, Moss Adams LLP)

San Diego, CA

June 24, 2025