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Finite-element numerical modeling and analysis of electromagnetic waveguides and resonators used in terahertz quantum cascade lasers are presented. Both metal-metal and semi-insulating (SI) surface-plasmon ridge waveguide geometries were investigated. Simulations and analysis of two types were performed: two-dimensional waveguides (eigenmode calculation), and two- and three-dimensional resonators (facet reflectivity calculation for infinite width and finite width waveguides, respectively). Waveguide simulations extend previous transverse one-dimensional analyses to two dimensions (for the lateral and transverse dimensions), and quantify the breakdown of the one-dimensional approximation as the ridge width is reduced. Resonator simulations in two and three dimensions are presented and are used to obtain facet reflectivities and output radiation patterns. For the metal-metal waveguide structures, these resonator simulations quantitatively show strong deviations for terahertz facet reflectivities from those predicted by the effective index method. However, the effective index method for calculating reflectivities is shown to still be valid for SI surface-plasmon waveguides.