Certain dielectric oxide single crystals display very low loss at microwave frequencies. On cooling the loss is generally observed to drop. The Q of sapphire at 10 GHz exceeds 10(6) 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, TiO2 and Zr0.875Sn0.25Ti0.875O4 (ZTS) are reported. Al2O3 and TiO2 have been studied as a model materials for dielectric loss. Theory predicts that the loss in single crystal sapphire should follow a T-5 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 T-5 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 > 5.5x10(4) at 10 GHz and at room temperature are possible and Q's well in excess of 10(5) at 10 GHz and 77 K can be achieved in a design made compact by the use of a HTS thick film shield.