This work presents a theoretical analysis of a hollow waveguide with an arbitrarily shaped cross section, with straight longitudinal axis, and truncated by impedance boundary condition. Additionally, mathematical models for the electromagnetic characterization of guided millimeter waves are developed to apply the point matching method to solve the boundary value problem. In this context, a first-order Leontovich boundary condition is initially studied to determine the electromagnetic fields in a tunnel. To enhance the accuracy of the approximate solution of the Leontovich boundary condition, the use of the first-order Rytov boundary condition is proposed, considering the system’s geometry (contour curvature). An algorithm involving the point matching technique was implemented in Matlab platform for the electromagnetic analysis inside the waveguide considering a constant surface impedance. The results of field propagation for different modes and conductivities are presented, discussed, and compared with finite element reference solutions.