EXHIBIT 32.1

                                 CERTIFICATION
      PURSUANT TO 18 U.S.C SECTION 1350 AS ADOPTED PURSUANT TO SECTION 906
                       OF THE SARBANES-OXLEY ACT OF 2002

         Pursuant to 18 U.S.C. Section 1350 as adopted pursuant to Section 906
of the Sarbanes-Oxley Act of 2002, each of the undersigned officers of Rand
Capital Corporation (the "Company"), does hereby certify, to such officer's
knowledge, that:

         The Quarterly Report on Form 10-Q for the quarter ended September 30,
2004 (the Form 10-Q) of the Company fully complies with the requirement of
section 13(a) or 15(d) of the Securities Exchange Act of 1934 and the
information contained in the Form 10-Q fairly presents, in all material
respects, the financial condition and results of operations of the Company.

  Dated: November 10, 2004

                                                /s/ Allen F. Grum
                                            --------------------------
                                             Allen F. Grum, President
                                            (Chief Executive Officer)


  Dated: November 10, 2004

                                                /s/ Daniel P. Penberthy
                                            ------------------------------
                                            Daniel P. Penberthy, Treasurer
                                              (Chief Financial Officer)