In this work, a proper orthogonal decomposition (POD) method is applied to time-domain Maxwell’s equations coupled to a Drude dispersion model, which are discretized in space by a discontinuous Galerkin (DG) method. An auxiliary differential equation (ADE) method is used to represent the constitutive relation for the dispersive medium. A POD–DGTD formulation with lower dimension and sufficiently high accuracy is established, together with the description of the POD reduced-order basis, its construction from a snapshot set, and its application to the solution of the time-domain Maxwell’s equations. The overall goal is to reduce the computational time while maintaining an acceptable level of accuracy, in order to obtain an efficient time-domain solver to be used as a starting-point for an optimization strategy. We provide results from numerical experiments for two-dimensional problems that illustrate the capabilities of the proposed POD–DGTD formulation and assess its efficiency.