A method for measuring by means of indicators based on garnet ferrite films the strong magnetic stray fields having intensities of 5–10 kOe that arise in systems of magnets with enormous magnetic anisotropy is described. The method is based on the phase transition from a strip domain structure into a uniformly magnetized state that takes place in garnet ferrite films in magnetic fields with intensities approaching the values of their anisotropy fields. It is shown that, by using indicators with various anisotropy field values, it is possible to obtain a fairly complete pattern of the stray fields localized in a narrow region over the magnets. The resolution limit in the localization region of a strong field is comparable to the width of the strip domains in the indicator and is 1–4 µm. The limiting value of the measured field intensity is equal to the anisotropy field of the indicator material.