Collimation of monochromatic beams of spin waves results from refraction at the interface between two magnetic half-planes. Collimation occurs for a broad range of the angles of incidence for homogenous Co and Permalloy (Py) halfplanes due to the intrinsic anisotropy of spin-wave propagation in these materials. The effect arises in samples saturated by an in-plane magnetic field tangential to the interface. Further, collimation for all possible angles of incidence occurs in a system where the incident spin wave is refracted at the interface between homogeneous and periodically patterned layers of yttrium–iron garnet (YIG). The refraction was investigated by the analysis of isofrequency dispersion contours for both pairs of materials (Co/Py and uniform YIG/patterned YIG), which are calculated by the plane-wave method. In addition, refraction in the Co/Py system was studied with micromagnetic simulations.