Epitaxial trilayer heterostructures of YBa2Cu3O7−&dgr;/BaxSr1−xTiO3/YBa2Cu3O7−&dgr;were grown on silicon‐on‐sapphire buffered by a double layer of CeO2/Y–ZrO2. Such structures may be considered for tunable microwave filters. The top and bottom YBa2Cu3O7−&dgr;films were wellc‐axis oriented, free from microcracks and had superconducting transitionsTc’s in the range 86–90 K. A thin antidiffusion layer of SrTiO3(d≊70 A˚) between YBa2Cu3O7−&dgr;and BaxSr1−xTiO3(x=0.25–0.9) promoted better crystallinity and higherTcof the top superconducting film. An Ag/BaxSr1−xTiO3/YBa2Cu3O7−&dgr;capacitor structure was used to determine the dielectric permittivity and the high frequency loss tan &dgr; of the BaxSr1−xTiO3layer. Maximum values of the permittivity of the BaxSr1−xTiO3layers were observed around the Curie temperatures of corresponding bulk monocrystals. The dielectric permittivity of the BaxSr1−xTiO3(x=0.25–0.75) layers depended strongly (≊20%) on an applied voltage (±2.5 V) at temperatures around 77 K. The tan &dgr; was much higher in films than in bulk crystals. ©1995 American Institute of Physics.