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, May 18, 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 $3,238,530.56 or $0.069483 per unit, based principally upon production during the month of March 2012. The distribution is payable June 14, 2012, to unit holders of record as of May 31, 2012.

Gas production for the properties from which the royalty was carved (the “Underlying Properties”) totaled approximately 2,704,138 Mcf (2,969,084 MMBtu). Dividing revenues by production volume yielded an average gas price for March 2012 of $3.52 per Mcf ($3.21 per MMBtu) as compared to $3.49 per Mcf ($3.19 per MMBtu) for February 2012. 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 $1,921,873. Lease operating expenses were $2,440,459 and taxes were $940,444.

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