Microwave-frequency (rf) power-dependence measurements performed on thin-film YBa2Cu3O7−δ grain boundaries engineered on sapphire bicrystal substrates with misorientation angles of θ = 2°, 5°, 10°, and 24° are presented. The data are compared to measurements on films grown on single-crystal substrates. A stripline-resonator measurement technique is employed. The rf results are compared to dc measurements performed on a four-point test structure on the same substrate as the resonator. The measurements demonstrate that low-angle grain boundaries (θ ⩽ 10°) have little effect on the rf power handling, while the high-angle grain boundaries (θ = 24°) cause large nonlinear losses due to Josephson vortices created by rf currents. © 1998 American Institute of Physics.