Exhibit 32.1

CERTIFICATION OF PRINCIPAL EXECUTIVE OFFICER

AND PRINCIPAL FINANCIAL OFFICER

PURSUANT TO 18 U.S.C. SECTION 1350

In connection with the Annual Report on Form 10-K of RAMTRON INTERNATIONAL CORPORATION for the year ended December 31, 2010, I, Eric A. Balzer, Chief Executive Officer and Chief Financial Officer of RAMTRON INTERNATIONAL CORPORATION, hereby certify pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, to the best of my knowledge and belief, that:

(1) such Annual Report on Form 10-K of RAMTRON INTERNATIONAL CORPORATION for the year ended December 31, 2010, fully complies with the requirements of section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

(2) the information contained in such Annual Report on Form 10-K of RAMTRON INTERNATIONAL CORPORATION for the year ended December 31, 2010, fairly presents, in all material respects, the financial condition and results of operations of RAMTRON INTERNATIONAL CORPORATION as of the dates and for the periods expressed in the report.

March 9, 2011

A signed original of this written statement required by Section 906 has been provided to Ramtron International Corporation and will be retained by Ramtron International Corporation and furnished to the Securities and Exchange Commission or its staff upon request.