Exhibit 99.1

San Juan Basin Royalty Trust

News Release

Compass Bank, Trustee

300 W. 7^th Street, Suite B

Fort Worth, Texas 76102

San Juan Basin Royalty Trust

Declares Monthly Cash Distribution

FORT WORTH, Texas, March 20, 2012 — Compass Bank, as Trustee of the San Juan Basin Royalty Trust (NYSE:SJT), today declared a monthly cash distribution to the holders of its units of beneficial interest of $4,009,660.40 or $0.086028 per unit, based principally upon production during the month of January 2012. The distribution for March includes granted audit exceptions of $405,381 including a $279,849 adjustment for the over-accrual of ad valorem taxes. The distribution is payable April 13, 2012, to unit holders of record as of March 30, 2012.

Gas production for the properties from which the royalty was carved (the “Underlying Properties”) totaled approximately 2,706,799 Mcf (2,973,172 MMBtu). Dividing revenues by production volume yielded an average gas price for January 2012 of $4.07 per Mcf ($3.70 per MMBtu) as compared to $4.49 per Mcf ($4.18 per MMBtu) for December 2011. The average gas price may vary from the posted index price for the San Juan Basin. The index price is a gross sales price, and the revenues used in the calculation of average gas prices are net of transportation, processing and gathering costs. Furthermore, the distribution to the Trust in any given month may include significant volume adjustments for sales in prior months that reflect pricing for those prior months. Capital costs for the month were $2,470,425. Lease operating expenses were $2,644,480 and taxes were $806,115.

Compass Bank

Lee Ann Anderson, Vice President & Senior Trust Officer

Kaye Wilke, Investor Relations, toll-free: (866) 809-4553

Fax: (817) 735-0936

Website: www.sjbrt.com

e-mail: sjt@compassbank.com