6-K

Dated: May 27, 2025

CAPITAL CLEAN ENERGY CARRIERS CORP.

/s/ Gerasimos (Jerry) Kalogiratos

Name: Gerasimos (Jerry) Kalogiratos

Title: Chief Executive Officer

UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

WASHINGTON, D.C. 20549

FORM 6-K

REPORT OF FOREIGN PRIVATE ISSUER

Pursuant to Rule 13a-16 or 15d-16

under the Securities Exchange Act of 1934

For the month of May 2025

COMMISSION FILE NUMBER: 001-33373

CAPITAL CLEAN ENERGY CARRIERS CORP.

(Translation of registrant’s name into English)

3 Iassonos Street

Piraeus, 18537 Greece

(Address of principal executive offices)

Indicate by check mark whether the Registrant files or will file annual reports under cover of Form 20-F or Form 40-F.

Form 20-F ☒ Form 40-F ☐

Attached as Exhibit I are the financial results of Capital Clean Energy Carriers Corp. (“CCEC”) for the three-month period ended March 31, 2025 and the related Operating and Financial Review and Prospects discussion.

Attached as Exhibit II is the following Unaudited Interim Condensed Consolidated Financial Statements of CCEC:

(i)	Unaudited Condensed Consolidated Balance Sheets as of March 31, 2025 and December 31, 2024

(ii)	Unaudited Condensed Consolidated Statements of Comprehensive Income for the three-month periods ended March 31, 2025 and 2024

(iii)

Unaudited Condensed Consolidated Statements of Changes in Shareholders’ Equity and Partners’ Capital for the three-month periods ended March 31, 2025 and 2024

(iv)	Unaudited Condensed Consolidated Statements of Cash Flows for the three-month periods ended March 31, 2025 and 2024

(v)	Notes to the Unaudited Interim Condensed Consolidated Financial Statements

This report on Form 6-K is hereby incorporated by reference into the registrant’s Registration Statement on Form F-3 (File No. 333-282610) and Registration Statement on Form F-3 (File No. 333-286825).

SIGNATURES

Pursuant to the requirements of the Securities Exchange Act of 1934, the registrant has duly caused this report to be signed on its behalf by the undersigned, thereunto duly authorized.