Exhibit 32.1

CERTIFICATIONS OF CHIEF EXECUTIVE OFFICER AND CHIEF FINANCIAL

OFFICER PURSUANT TO 18 U.S.C. SECTION 1350 AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

Pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, each of Frank J. Del Rio, the President and Chief Executive Officer, and Wendy A. Beck, the Executive Vice President and Chief Financial Officer, of Norwegian Cruise Line Holdings Ltd. (the “Company”), does hereby certify, that, to such officer’s knowledge:

The annual report on Form 10-K of the Company, for the fiscal year ended December 31, 2014 (the “Form 10-K”), fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934 and information contained in the Form 10-K fairly presents, in all material respects, the financial condition and results of operations of the Company.

Date: February 27, 2015