To support the development of clinical applications of high-frequency ultrasound, appropriate tissue-mimicking materials (TMMs) are required whose acoustic properties have been measured using validated techniques. This paper describes the characterisation of the sound speed (phase velocity) and attenuation coefficient of the International Electrotechnical Commission (IEC) agar-based TMM over the frequency range 1 to 60 MHz. Measurements implemented a broadband through-transmission substitution immersion technique over two overlapping frequency ranges, with co-axially aligned 50 MHz centre-frequency transducers employed for characterisation above 15 MHz. In keeping with usual practice employed within the technical literature, thin acoustic windows (membranes) made of 12-μm-thick Mylar protected the TMM from water damage. Various important sources of uncertainty that could compromise measurement accuracy have been identified and evaluated through a combination of experimental studies and modelling. These include TMM sample thickness, measured both manually and acoustically, and the influence of interfacial losses that, even for thin protective membranes, are significant at the frequencies of interest. In agreement with previous reports, the attenuation coefficient of the IEC TMM exhibited non-linear frequency dependence, particularly above 20 MHz, yielding a value of 0.93 ± 0.04 dB cm(-1) MHz(-1) at 60 MHz, derived at 21 ± 0.5°C. For the first time, phase velocity, measured with an estimated uncertainty of ±3.1 m s(-1), has been found to be dispersive over this extended frequency range, increasing from 1541 m s(-1) at 1 MHz to 1547 m s(-1) at 60 MHz. This work will help standardise acoustic property measurements, and establishes a reference measurement capability for TMMs underpinning clinical applications at elevated frequencies.