We present a novel coordinate transformation technique that controls the propagation of waves inside a waveguide, such that the waveguide behaves as if it is a reshaped waveguide. In this technique, the spatial domain of the waveguide is mapped to that of its reshaped equivalent, yielding an anisotropic medium inside the waveguide. In other words, the waveguide in the transformed space can be imagined as if it is filled with an anisotropic metamaterial whose spatially varying constitutive parameters reflect the effect of the coordinate transformation on the field quantities. In this anisotropic metamaterial, Maxwell's equations are still satisfied due to their form-invariance property under coordinate transformations. The most appealing feature of the proposed method is that it renders a waveguide to support electromagnetic wave propagation below the cutoff frequency; thus, it can be utilized in waveguide miniaturization. However, this technique is more general, and it can transform a waveguide into another waveguide having an arbitrary miniaturized (or maxiaturized) shape without changing its propagation characteristics. Thus, the proposed method can be employed for the elimination of discontinuities in abrupt waveguide-to-waveguide transitions. We report numerical results for finite element simulations of various waveguides.