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We report measurements and modeling of microwave-frequency vortex dynamics in YBCO grain boundaries that are modeled as long Josephson junctions by numerically solving the sine-Gordon equation. YBCO bicrystal grain boundaries with misorientation angles from 2 to 24° have been studied experimentally using microwave resonator measurement techniques. Comparison between the measured and calculated microwave impedance and the harmonic generation of the 24° grain boundaries indicates that the 24° grain boundaries are weakly coupled long Josephson junctions. The corresponding results of lower angle grain boundaries are also presented. A transition from strong-coupled single-crystal-like behavior to weak-coupled Josephson-junction-like behavior has been observed in a 10° grain boundary between 55 and 75 K. The physics of Josephson-vortex dynamics and its impact on the microwave properties of superconducting thin films are discussed.