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The combination of high Q dielectric resonators and high temperature superconducting (HTS) films offer many advantages in the area of cellular and satellite communications. The high cost of single crystal dielectrics and HTS thin films may be unattractive in certain applications. Superconducting thick films and polycrystalline ceramic dielectrics offer a high performance, low cost alternative to high Q thin film/single crystal dielectric resonators. Results on polycrystalline dielectrics show that Q's well in excess of 10/sup 5/ at 10 GHz and 77 K can be achieved in a design made compact by the use of a HTS thick film shield.