Exhibit 99.1

San Juan Basin Royalty Trust

News Release

Compass Bank, Trustee

300 West Seventh Street, Suite B

Fort Worth, Texas 76102

San Juan Basin Royalty Trust Declares

Monthly Cash Distribution

FORT WORTH, Texas, May 20, 2016 – 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 $123,447.02 or $0.002649 per Unit, based principally upon production during the month of March 2016. The distribution is payable June 14, 2016, to Unit Holders of record as of May 31, 2016.

Gas production for the properties from which the royalty was carved (the “Underlying Properties”) totaled approximately 2,438,062 Mcf (2,702,065 MMBtu). Dividing revenues by production volume yielded an average gas price for March 2016 of $1.32 per Mcf ($1.19 per MMBtu) as compared to $1.67 per Mcf ($1.52 per MMBtu) for February 2016.

The average monthly gas price Burlington reports to the Trust is a calculated price. It is determined by dividing gross monthly revenue by production volume, and therefore, it does not represent an average of actual sales prices. 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 $87,651. Lease operating expenses were $2,117,557 and taxes were $401,568.

Contact: San Juan Basin Royalty Trust

Compass Bank

Joshua R. Peterson, 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.us@bbva.com