The huge increase in the use of microwave communications places severe constraints on the operating performance of the microwave filters. Dielectric resonators are a very attractive option as they can be prepared with very low dielectric loss, moderately high dielectric constant and a low temperature coefficient of the resonant frequency. In filters they possess very low intermodulation products and are capable of handling high power. Certain dielectric oxide single crystals display very low loss at microwave frequencies and on cooling the loss is generally observed to drop. The Q of sapphire at 10 GHz exceeds 107 at low temperatures of around 10K. However, single crystals are expensive and the purpose of this research is to explore inexpensive, sintered polycrystalline alternatives. By very careful attention to purity, processing and microstructure Q values approaching those of single crystals have been achieved. The loss of polycrystalline ceramics of Al2O3, Ba(Mg1/3Ta2/3)O3 (BMT) and Zr0.875Sn0.25Ti0.875O4 (ZTS) has been studied. Alumina, Al2O3 has been studied as a model material for dielectric loss. Theory predicts that the loss in single crystal sapphire should follow a T5 dependence. However at low temperatures the loss is dominated by extrinsic losses due to crystal imperfection, residual dopant atoms, dislocations and other lattice defects and the T5 dependence does not hold. In polycrystalline alumina the intrinsic loss is immediately masked by these extrinsic losses, even at room temperature, and a simple T dependence is observed. Results on polycrystalline alumina show that a Q of > 5×104 at 10 GHz and at room temperature are possible and Q's well in excess of 105 at 10 GHz and 77 K can be achieved.