The method of numerical micromagnetic simulation was used to study the magnetization dynamics of a thin film with uniaxial magnetic anisotropy during ferromagnetic resonance (FMR) excitation in it on the local sites by a linearly polarized high-frequency magnetic field emitted from the 1 mm opening in the metallic screen of the transmission line. It was established that non-uniformities of demagnetizing fields emerging near the film edges lead not only to the change in the FMR field, but also to the change in the value and direction of the uniaxial anisotropy field. The distribution of non-uniformities of the magnetic anisotropy characteristics over the area of 60 nm thick permalloy film that was measured on the scanning FMR spectrometer agrees well with the micromagnetic simulation results. Demagnetizing fields were proved to be the main cause for the edge effects in magnetic films.