EXHIBIT 32.1

CERTIFICATION OF

PRINCIPAL EXECUTIVE OFFICER

PURSUANT TO 18 U.S.C. SECTION 1350

(SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002)

In connection with the accompanying Annual Report on Form 10-K of Maxwell Technologies, Inc. for the year ended December 31, 2009, I, David J. Schramm, Chief Executive Officer of Maxwell Technologies, Inc., hereby certify pursuant to 18 U.S.C. § 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that to the best of my knowledge:

(1) such Annual Report on Form 10-K of Maxwell Technologies, Inc. for the year ended December 31, 2009, 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 such Annual Report on Form 10-K of Maxwell Technologies, Inc. for the year ended December 31, 2009, fairly presents, in all material respects, the financial condition and results of operations of Maxwell Technologies, Inc. at the dates indicated.

This certification has not been, and shall not be deemed, “filed” with the Securities and Exchange Commission.

A signed copy of this written statement required by Section 906 has been provided to Maxwell Technologies, Inc. and will be retained by Maxwell Technologies, Inc. and furnished to the Securities and Exchange Commission or its staff upon request.