EXHIBIT 32.1 CERTIFICATION BY CHIEF EXECUTIVE OFFICER PURSUANT TO 18 U.S.C. SECTION 1350, AS ADOPTED PURSUANT TO SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002 In connection with the Amendment No. 2 to the Quarterly Report of Research Frontiers Incorporated (the Company) on Form 10-Q/A for the quarterly period ending March 31, 2004 as filed with the Securities and Exchange Commission on the date hereof (the Report), I, Robert L. Saxe, Chairman and Chief Executive Officer of the Company, certify, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 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; and (2) The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the issuer. /s/ Robert L. Saxe Robert L. Saxe Chairman and Chief Executive Officer October 28, 2004