The reduced basis method (RBM) generates low order models for the solution of parametrized partial differential equations (PDEs) to allow for efficient evaluation in many-query and real-time contexts. We show the theoretical framework in which the RBM is applied to Maxwell\'s equations and present numerical results for model reduction in frequency domain. Using rigorous error estimators, the RBM achieves low order models under variation of material parameters and geometry. The RBM reduces model order by a factor of 50 to 100 and reduces compute time by a factor of 200 and more for numerical experiments using standard circuit elements.