Exhibit 99.1

San Juan Basin Royalty Trust

News Release

San Juan Basin Royalty Trust Declares December Cash Distribution

FORT WORTH, Texas, December 20, 2018 – Compass Bank, as Trustee of the San Juan Basin Royalty Trust (the “Trust”) (NYSE:SJT), today declared a monthly cash distribution to the holders of its Units of beneficial interest (the “Unit Holders”) of $1,125,838.13 or $0.024155 per Unit, based primarily upon production during the month of October 2018, subject to certain adjustments by the operator of the Trust’s subject interests, Hilcorp San Juan L.P. (“Hilcorp”), for prior months. The distribution is payable January 15, 2019, to Unit Holders of record as of December 31, 2018.

Based upon information provided to the Trust by Hilcorp, gas production for the subject interests totaled 2,568,161 Mcf (2,853,512 MMBtu) for October 2018, as compared to 2,444,542 Mcf (2,716,158 MMBtu) for September 2018. Dividing revenues by production volume yielded an average gas price for October 2018 of $2.08 per Mcf ($1.88 per MMBtu), as compared to an average gas price for September 2018 of $2.21 per Mcf ($1.99 per MMBtu).

Hilcorp has advised the Trust that for the reporting month of October 2018, oil and gas production was accrued based on actual production volumes, including an estimate of $169,000 for non-operated revenue. For the month ended October 2018, Hilcorp reported to the Trust capital costs of $794,463, lease operating expenses and property taxes of $2,605,778 and severance taxes of $617,463.

Except for historical information contained in this news release, the statements in this news release are forward-looking statements that are made pursuant to the Safe Harbor Provisions of the Private Securities Litigation Reform Act of 1995. Such forward-looking statements generally are accompanied by words such as “estimates,” “anticipates,” “could,” “plan,” or other words that convey the uncertainty of future events or outcomes. Forward-looking statements and the business prospects of San Juan Basin Royalty Trust are subject to a number of risks and uncertainties that may cause actual results in future periods to differ materially from the forward-looking statements. These risks and uncertainties include, among other things, certain information provided to the Trust by Hilcorp, volatility of oil and gas prices, governmental regulation or action, litigation, and uncertainties about estimates of reserves. These and other risks are described in the Trust’s reports and other filings with the Securities and Exchange Commission.