Exhibit 32.1

MCDERMOTT INTERNATIONAL, INC.

Certification Pursuant to

Section 906 of the Sarbanes-Oxley Act of 2002

(Subsections (a) and (b) of Section 1350, Chapter 63 of Title 18, United States Code)

Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002 (Subsections (a) and (b) of Section 1350, Chapter 63 of Title 18, United States Code), I, Stephen M. Johnson, Chief Executive Officer of McDermott International, Inc., a Panamanian corporation (the “Company”), hereby certify, to my knowledge, that:

(1) the Company’s Quarterly Report on Form 10-Q for the quarter ended June 30, 2012 (the “Report”) fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

(2) information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Dated: August 6, 2012

/s/ Stephen M. Johnson

Stephen M. Johnson

Chairman of the Board of Directors, President and Chief Executive Officer