EXHIBIT 31

CERTIFICATION

I, Joshua R. Peterson,
certify that:

1.    I have reviewed this Quarterly Report on Form 10-Q of San
Juan Basin Royalty Trust, for which Compass Bank acts as Trustee;

2.    Based on my knowledge, this 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
report;

3.    Based on my knowledge, the financial statements, and other financial information included in this
report, fairly present in all material respects the financial condition, distributable income and changes in trust corpus of the registrant as of, and for, the periods presented in this report;

4.    I am 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 I have:



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



| | b) | Designed such internal control over financial reporting, or caused such internal control over financial reporting to be designed under my supervision, to provide reasonable assurance regarding the reliability of
financial reporting and the preparation of financial statements for external purposes;
| | -- | ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------



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



| | d) | Disclosed in this 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.    I have disclosed, based on my most recent evaluation of internal control over financial reporting, to the
registrants auditors:



| | 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 persons who have a significant role in the registrants internal control over financial reporting.
| | -- | ----------------------------------------------------------------------------------------------------------------------------------------------------



|                   |  |  |  |     |  |                                         
|------------------ |  |  |  | --- |  | ----------------------------------------
|Date: May 10, 2018 |  |  |  | By: |  | /s/ Joshua R. Peterson                  
|                   |  |  |  |     |  | Joshua R. Peterson                      
|                   |  |  |  |     |  | Vice President and Senior Trust Officer,
|                   |  |  |  |     |  | Compass Bank