The paper examines the effect of an external magnetic field on inhomogeneous magnetic structures formed in the region of a pair of closely spaced holes in a ferromagnetic film with strong easy-plane anisotropy. It is shown that the impact of a field normal to the film plane can lead either to the destruction of a vortex-like structure when the field strength exceeds a certain critical value, or to transformation of the magnetic structure without changing its topology. Such a transformation is associated with the deviation of the magnetization vector from the film plane, and the greatest deviation is observed in the gap between the perforations near their boundaries. The features of magnetization distributions formed under the influence of an external field have been studied both by analytical methods within the framework of approximate models (weak field approximation, single antidot model, “pretzel” model) and by numerical simulation.