Exhibit 32.1

CERTIFICATION PURSUANT TO

18 U.S.C. SECTION 1350,

AS ADOPTED BY SECTION 906

OF THE SARBANES-OXLEY ACT OF 2002

Each of the undersigned hereby certifies, pursuant to 18 U.S.C. § 1350, in his capacity as an officer of Diamond Offshore Drilling, Inc. (the “Company”), that, to his knowledge:

(1) the Company’s Annual Report on Form 10-K for the fiscal year ended December 31, 2015, as filed with the U.S. Securities and Exchange Commission on the date hereof (the “Report”), fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended; and

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

Dated: February 19, 2016

/s/ Marc Edwards

Marc Edwards,

Chief Executive Officer of the Company

/s/ Gary T. Krenek

Gary T. Krenek,

Chief Financial Officer of the Company