Exhibit 23.1

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We consent to the incorporation by reference in this Registration Statement on Form F-3 of our reports dated April 17, 2025, relating to the financial statements of Capital Clean Energy Carriers Corp., and the effectiveness of Capital Clean Energy Carriers Corp.’s internal control over financial reporting, appearing in the Annual Report on Form 20-F of Capital Clean Energy Carriers Corp. for the year ended December 31, 2024. We also consent to the reference to us under the heading “Experts” in such Registration Statement.

/s/ Deloitte Certified Public Accountants S.A.

Athens, Greece

June 10, 2025