Exhibit 15.1

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We consent to the incorporation by reference in Registration Statement Nos. 333-282610, 333-286825 and 333-287895 on Form F-3 of our reports dated April 27, 2026, relating to the consolidated 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 this Annual Report on Form 20-F for the year ended December 31, 2025.

/s/ Deloitte Certified Public Accountants S.A.

Athens, Greece

April 27, 2026