We present the Discontinuous Galerkim methods for solving Time-Domain (DGTD) Maxwell's equations coupled to the Drude model arising from nanophotonics. Model Order Reduction (MOR) techniques are employed to reduce the simulation time. We have considered a Proper Orthogonal Decomposition (POD) method, Krylov-subspace based operator exponential approach and Padé approximation approach. Numerical results show that the proposed DGTD + MOR methodology is much faster than the full DGTD methods.