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, August 21, 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 $1,683,585.01 or $0.036122 per unit, based principally upon production during the month of June 2012. The distribution is payable September 17, 2012, to unit holders of record as of August 31, 2012.

The distribution for August was reduced by $742,779 as a result of an adjustment of lease operating expense and capital costs that were understated in the April 2012 distribution as a result of a miscalculation by Burlington Resources Oil & Gas Company LP (“Burlington.”) The miscalculation resulted in overpayments to the trust for April through July 2012. As previously disclosed, and as permitted under the terms of the Royalty conveyance document, Burlington intends to also adjust lease operating expense and capital costs during the months of September through November 2012 to recover the overpayments.

Gas production for the properties from which the royalty was carved (the “Underlying Properties”) totaled approximately 2,547,320 Mcf (2,800,125 MMBtu). Dividing revenues by production volume yielded an average gas price for June 2012 of $2.70 per Mcf ($2.46 per MMBtu) as compared to $2.46 per Mcf ($2.25 per MMBtu) for May 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 $1,031,922. Lease operating expenses were $3,200,729 and taxes were $723,137.

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