Epitaxial thin films of YBa2Cu3O7have been prepared on SrTiO3and LaAlO3substrates by a high‐pressure planar dc‐sputtering technique. By covering the substrate heater with a frame of polycrystalline YBa2Cu3O7substantial improvements of the YBa2Cu3O7film properties were achieved. These are characterized by dc‐resistivity values &rgr;(T) of less than 50 &mgr;&OHgr; cm at 100 K and &rgr;(300 K)/&rgr;(100 K) values of up to 3.9. Significant deviations from the usual linear &rgr;(T) behavior were found. Critical temperatures above 90 K, resistive transition widths down to 0.3 K, and critical current densities of about 5 × 106A/cm2at 77 K confirm the high quality of the films. As indicated by Rutherford backscattering and high‐resolution transmission electron microscopy the films exhibit a microstructure characterized by a reduced density of lattice defects. However, lattice‐coherent precipitates with a diameter of about 5–10 nm were observed. As an outstanding feature the films exhibit, besides the initial steep falloff atTc, a further gradual decrease of the microwave surface resistance at 87 GHz below 50 K by at least one order of magnitude. These results are very promising for millimeter‐wave applications of epitaxial YBa2Cu3O7thin films.