There are many techniques available for characterising the complex permittivity of microwave dielectric ceramics as functions of temperature and frequency. For materials with modest dielectric loss (\(\tan \delta > 10^{-3}\)) broadband transmission line measurements can yield the complex permittivity with reasonable accuracy over a wide frequency range. However, for very low loss dielectrics (\(\tan \delta < 10^{-4}\)) such as the ones studied here, a dielectric resonator technique is required. A dielectric resonator consists of a cylindrical dielectric sample mounted upon a low-loss, low-permittivity support such as quartz or polystyrene, housed within a conducting metallic cylindrical cavity.