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:
    November 6, 2020 |                                             
|--------------------------- | --------------------------------------------
|                            |                                             
|                            | /s/
    Allen F. Grum                       
|                            | Allen
    F. Grum, President                
|                            | (Chief
    Executive Officer of Rand Capital
|                            | Corporation)