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Guiding properties of an optical waveguide based on a layered metamaterial formed by layers of iron-yttrium garnet and aluminum-yttrium garnet, magnetized to saturation are considered. Dispersion equations for the waveguide TE and TM modes in the structure were obtained using the approximation of an effective medium and solving the boundary problem (electromagnetic method), and also by means of a 4×4 matrix method. Dispersion spectra of the propagation constant dependence on the cyclic frequency ω(β) for different types of structures are found, localization coefficients of the orthogonal modes in the guiding layer are also derived and their comparative analysis is carried out. The advantages of the approximate electromagnetic method are shown in comparison with the exact 4x4 matrix method. The results of the work can find an application in developing new integrated optical devices for optical signal processing based on layered metamaterials.