EXHIBIT 31

CERTIFICATION

I, Lee
Ann Anderson, 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.
| | -- | ----------------------------------------------------------------------------------------------------------------------------------------------------

In giving the certifications in paragraphs 4 and 5 above, I have relied to the extent I consider
reasonable on information provided to me by Burlington Resources Oil & Gas Company LP.



|      |  |                |  |  |  |     |  |                                                                       
|----- |  | -------------- |  |  |  | --- |  | ----------------------------------------------------------------------
|Date: |  | August 9, 2012 |  |  |  | By: |  | /s/ Lee Ann Anderson                                                  
|      |  |                |  |  |  |     |  | Lee Ann Anderson Vice President and Senior Trust Officer, Compass Bank