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Hexagonal barium ferrite films with thickness between 0.3 and 8 μm were deposited on (0001) oriented Al2O3 using pulsed laser deposition and optimized growth and annealing conditions. They were characterized by measurements of x-ray diffraction, Rutherford backscattering, magnetization, atomic force microscopy and ferromagnetic resonance (FMR) at 58 GHz. The narrowest FMR lines and largest number of spin wave resonances are obtained when the field is perpendicular to the film plane of 0.3 and 0.46 μm films. To quantitatively account for variations with field angle (θ) we assume (i) a strain-induced anisotropy energy with cos4 θ dependence and (ii) that the film should be pictured as a mosaic whose tiles are tilted out of the film plane.