This study presents a computational method for modeling electromagnetic fields in curved rectangular waveguides with uniform cross-section, using the variational Rayleigh-Ritz method. The potential applications of this research in engineering include the design of feeders for antennas, microwave mode converter devices, filters, among others. While various models have been proposed to solve this problem, conventional numerical techniques based on finite elements, finite differences, and finite volumes require high computational costs. To overcome these issues, a variational formulation for solving Maxwell s equations in a local toroidal coordinate system was developed via a novel functional introduced in this work. The functional was adapted to handle uniformly bend domains with arbitrary cross-section, and analytical investigations were conducted to confirm its stationary characteristics. The Rayleigh-Ritz formalism was employed to convert the functional into an equivalent problem of eigenvalues and eigenvectors using an expansion in terms of rectangular harmonics of a straight waveguide as basis functions for modeling a bend rectangular waveguide. A numerical algorithm was developed in Matlab to validate our model, and the results were compared against reference perturbational and numerical solutions, demonstrating high accuracy and lower computational costs.