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We examine parallel-plate magnetic photonic crystal (MPC) waveguides comprised of a periodic loading with two anisotropic layers and one ferrite layer on each period. It is shown that, at a specific design frequency , parallel-plate MPC waveguides can support a Bloch mode with zero axial group velocity similar to the ldquofrozen moderdquo regime of the prototypical 1D MPC structure. When the proposed 2D structure is illuminated with a properly polarized time-harmonic wave, near unity power transmission (coupling) into the frozen mode occurs, and field strength within the MPC becomes orders of magnitude larger than the incident field strength. The steady-state case is evaluated using both analytical tools and finite elements, while the finite-difference time-domain method is applied to evaluate the 2D MPC transient response.