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We introduce a new approach which enables a waveguide to support propagation of electromagnetic waves below the cutoff frequency, as well as which avoids undesirable reflections in a waveguide. These are achieved through the usage of an anisotropic metamaterial layer by employing the concept of coordinate transformation. The proposed method can be utilized for the fabrication of miniaturized waveguides, and for the elimination of discontinuities in abrupt waveguide transitions. We demonstrate some numerical experiments for finite element simulations of parallel-plate and dielectric slab waveguides.