Method and apparatus are provided for propagating microwave energy into heart tissues to produce a desired temperature profile therein at tissue depths sufficient for thermally ablating arrhythmogenic cardiac tissue to treat ventricular tachycardia and other arrhythmias while preventing excessive heating of surrounding tissues, organs, and blood. A wide bandwidth double-disk antenna (700) is effective for this purpose over a bandwidth of about six gigahertz. A computer simulation provides initial screening capabilities for an antenna such as antenna, frequency, power level, and power application duration. The simulation also allows optimization of techniques for specific patients or conditions. In operation, microwave energy between about 1 Gigahertz and 12 Gigahertz is applied to monopole microwave radiator (600) having a surface wave limiter (606). A test setup provides physical testing of microwave radiators (854) to determine the temperature profile created in actual heart tissue or ersatz heart tissue (841). Saline solution (872) pumped over the heart tissue (841) with a peristaltic pump (862) simulates blood flow. Optical temperature sensors (838) disposed at various tissue depths within the heart tissue (841) detect the temperature profile without creating any electromagnetic interference. The method may be used to produce a desired temperature profile in other body tissues reachable by catheter (510) such as tumors and the like.