UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

WASHINGTON, D.C.

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 is a table setting forth the capitalization and indebtedness of Capital Clean Energy Carriers Corp. as of March 31, 2025.

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.

	CAPITAL CLEAN ENERGY CARRIERS CORP.
Dated: May 29, 2025	/s/ Gerasimos (Jerry) Kalogiratos
	Name: Gerasimos (Jerry) Kalogiratos
	Title: Chief Executive Officer