Summary: A methodology, termed variational electromagnetics, is introduced for handling time-harmonic linear electromagnetic field problems. First a desired variational formulation is derived from a fundamental variational principle and then is solved by the hybrid element method along with the frontal solution algorithm. The main advantages of such an approach are the unified derivation of variational equations for both interior and exterior field problems and their efficient numerical solution, especially for problems with inhomogeneous media. Also included is a numerical example in which the scattering from an inhomogeneously coated cylinder is analyzed.