The work described in this paper is intended to provide a basis for the design of a controlled rewarming system for cryopreserved tissues and organs using electromagnetic energy. For rapid rewarming (say, > 10 °C/min), the temperature distribution in the organ is effectively determined by the uniformity (or otherwise) of the power deposition, which is in turn controlled by the electrical properties of the perfused tissue. In this contribution, we describe the measurement system we have used to characterize the electrical properties of perfusates and perfused rabbit kidney tissue from −30 to + 20 °C. Measurements have been made on three perfusates using an open-ended coaxial probe sensor over a continuous range of radio and microwave frequencies covering 50 MHz to 2.6 GHz. Results show that the behavior of the electrical properties with increasing temperature is unfavorable at either end of the frequency range investigated—either the power absorption has a positive temperature coefficient or the penetration depth is too shallow. However, there is a compromise frequency range, determined in part by the perfusate composition, where these factors are much less serious. In this frequency range, the electrical properties of the perfused tissue are dominated by the properties of the perfusate. Modifications to the perfusate composition, e.g., reducing the concentration of electrolytes by adding sucrose, can further improve the temperature dependence of the electrical properties.