Exhibit 32.1

CERTIFICATION PURSUANT TO

RULE 13a-14(b) OF THE SECURITIES EXCHANGE ACT OF 1934

AND 18 U.S.C. SECTION 1350

In connection with the Annual Report of Tessera Technologies, Inc., a Delaware corporation (the “Company”), on Form 10-K for the year ending December 31, 2009 as filed with the Securities and Exchange Commission (the “Report”), I, Henry R. Nothhaft, President and Chief Executive Officer of the Company, certify, pursuant to Rule 13a-14(b) of the Securities Exchange Act of 1934 and 18 U.S.C. § 1350, as adopted pursuant to § 906 of the Sarbanes-Oxley Act of 2002, that to my knowledge:

(1) 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 result of operations of the Company.

CERTIFICATION PURSUANT TO

RULE 13a-14(b) OF THE SECURITIES EXCHANGE ACT OF 1934

AND 18 U.S.C. SECTION 1350

In connection with the Annual Report of Tessera Technologies, Inc, a Delaware corporation (the “Company”), on Form 10-K for the year ending December 31, 2009 as filed with the Securities and Exchange Commission (the “Report”), I, Michael Anthofer, Executive Vice President and Chief Financial Officer of the Company, certify, pursuant to Rule 13a-14(b) of the Securities Exchange Act of 1934 and 18 U.S.C. § 1350, as adopted pursuant to § 906 of the Sarbanes-Oxley Act of 2002, that to my knowledge:

(1) 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 result of operations of the Company.

A signed original of this written statement required by Rule 13a-14(b) of the Securities Exchange Act of 1934 and 18 U.S.C. Section 1350 has been provided to the Registrant and will be retained by the Registrant and furnished to the Securities and Exchange Commission or its staff upon request.