Surface resistance measurements of films of YBa 2 Cu 3 O 7 deposited onto single‐crystal substrates of LaGaO 3 and SrTiO 3 have been made at a frequency of 22 GHz. The measurements were made in either a copper or niobium cavity by replacing the end wall with the superconducting film. Typical surface resistance at 20 K are 1–2 mΩ for films on LaGaO 3 and 6–8 mΩ for films on SrTiO 3 , as measured in the copper cavity. The LaGaO 3 values lie within the sensitivity range of the Cu cavity (∼2 mΩ) and can only be considered upper limits. Similar measurements in a Nb superconducting cavity resulted in a surface resistance value of 0.2±0.1 mΩ at 4 K for the best LaGaO 3 ‐based film. This value is more than an order of magnitude lower than Cu, and suggests that LaGaO 3 ‐based films may offer immediate advantages in a number of applications.