Exhibit 99.1

Enduro Royalty Trust

Announces Monthly Cash Distribution

AUSTIN, Texas—(BUSINESS WIRE)—August 20, 2013

Enduro Royalty Trust (NYSE: NDRO) (the “Trust”) announced today a cash distribution to the holders of its units of beneficial interest of $0.162363 per unit, payable on September 16, 2013, to unitholders of record on August 30, 2013. The distribution primarily represents oil production during the month of May 2013 and natural gas production during April 2013.

The following table displays underlying oil and natural gas sales volumes and average prices attributable to the current and prior month distributions.

As oil and natural gas sales volumes reported to the Trust represent volumes for which Enduro Resource Partners was paid during the applicable month, reported volumes fluctuate due to the timing of cash receipts from operators. The significant increase in natural gas production reported above was due to approximately 258,000 Mcf that was paid by an operator during the current calculation period for 23 months of production from a well in north Louisiana. This resulted in $780,000 in additional natural gas revenues during the calculation period. Excluding this adjustment, realized natural gas prices for April production were $4.03 per Mcf.

Proceeds from the settlement of applicable hedge contracts related to the properties underlying the Trust were approximately $0.4 million, of which $0.1 million related to May 2013 oil hedges and $0.3 million related to June 2013 natural gas hedges.

Capital expenditures for the properties underlying the Trust during the period were approximately $0.4 million, which relates to expenses incurred during June 2013.

Enduro Royalty Trust is a Delaware statutory trust formed by Enduro Resource Partners to own a net profits interest representing the right to receive 80% of the net profits from the sale of oil and natural gas production from certain of Enduro Resource Partners’ properties in the states of Texas, Louisiana and New Mexico. As described in the Trust’s filings with the Securities and Exchange Commission, the amount of the periodic distributions is expected to fluctuate, depending on the proceeds received by the Trust as a result of actual production volumes, oil and gas prices and the amount and timing of the Trust’s administrative expenses, among other factors. Future distributions are expected to be made on a monthly basis. For additional information on the Trust, please visit www.enduroroyaltytrust.com.

Enduro Royalty Trust

Monthly Cash Distribution

This press release contains statements that are “forward-looking statements” within the meaning of Section 21E of the Securities Exchange Act of 1934, as amended. All statements contained in this press release, other than statements of historical facts, are “forward-looking statements” for purposes of these provisions. These forward-looking statements include the amount and date of any anticipated distribution to unitholders. The anticipated distribution is based, in part, on the amount of cash received or expected to be received by the Trust from Enduro Resource Partners with respect to the relevant period. Any differences in actual cash receipts by the Trust could affect this distributable amount. Other important factors that could cause actual results to differ materially include expenses of the Trust and reserves for anticipated future expenses. Statements made in this press release are qualified by the cautionary statements made in this press release. Neither Enduro Resource Partners nor the Trustee intends, and neither assumes any obligation, to update any of the statements included in this press release. An investment in units issued by Enduro Royalty Trust is subject to the risks described in the Trust’s filings with the SEC, including the risks described in the Trust’s Annual Report on Form 10-K for the year ended December 31, 2012, filed with the SEC on March 18, 2013. The Trust’s quarterly and other filed reports are or will be available over the Internet at the SEC’s website at http://www.sec.gov.

Contact

Enduro Royalty Trust

The Bank of New York Mellon Trust Company, N.A., as Trustee

Mike Ulrich, 1 (800) 852-1422

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