EXHIBIT 31.1



CERTIFICATION

Pursuant to Rules 13a-14(a)/15d-14(a)
under the Securities Exchange Act of 1934, as amended



I, Allen F. Grum, certify
that:



1. I have reviewed this quarterly
report on Form 10-Q of Rand Capital Corporation;



2. Based on my knowledge, this quarterly
report does not contain any untrue statement of a material fact or omit to state a material fact necessary to make the statements
made, in light of the circumstances under which such statements were made, not misleading with respect to the period covered by
this quarterly report;



3. Based on my knowledge, the financial
statements, and other financial information included in this quarterly report, fairly present in all material respects the financial
condition, results of operations and cash flows of the registrant as of, and for, the periods presented in this quarterly report;



4. The registrant’s other
certifying officer and I are responsible for establishing and maintaining disclosure controls and procedures (as defined in Exchange
Act Rules 13a-15(e) and 15d-15(e)) and internal control over financial reporting (as defined in Exchange Act Rules 13a-15(f) and
15d-15(f)) for the registrant and have:



a) Designed such disclosure controls
and procedures, or caused such disclosure controls and procedures to be designed under our supervision, to ensure that material
information relating to the registrant, including its consolidated subsidiaries, is made known to us by others within those entities,
particularly during the period in which this quarterly report is being prepared;



b) Designed such internal control over
financial reporting, or caused such internal control over financial reporting to be designed under our supervision, to provide
reasonable assurance regarding the reliability of financial reporting and the preparation of financial statements for external
purposes in accordance with generally accepted accounting principles;



c) Evaluated the effectiveness of the
registrant’s disclosure controls and procedures and presented in this quarterly report our conclusions about the effectiveness
of the disclosure controls and procedures, as of the end of the period covered by this quarterly report based on such evaluation;
and



d) Disclosed in this quarterly report
any change in the registrant’s internal control over financial reporting that occurred during the registrant’s most
recent fiscal quarter (the registrant’s fourth fiscal quarter in the case of an annual report) that has materially affected,
or is reasonably likely to materially affect, the registrant’s internal control over financial reporting; and



5. The registrant’s other
certifying officer and I have disclosed, based on our most recent evaluation of internal control over financial reporting, to the
registrant’s auditors and the audit committee of the registrant’s board of directors (or persons performing the equivalent
functions):



a) All significant deficiencies and
material weaknesses in the design or operation of internal control over financial reporting which are reasonably likely to adversely
affect the registrant’s ability to record, process, summarize and report financial information; and



b) Any fraud, whether or not
material, that involves management or other employees who have a significant role in the registrant’s internal control
over financial reporting.



|Dated: August 7, 2020 |                                                      
|--------------------- | -----------------------------------------------------
|                      | /s/ Allen F. Grum                                    
|                      | Allen F. Grum, President                             
|                      | (Chief Executive Officer of Rand Capital Corporation)