Summary: In [M. Fares, J. S. Hesthaven, Y. Maday and B. Stamm, J. Comput. Phys. 230, No. 14, 5532–5555 (2011; Zbl 1220.78045)], a reduced basis method (RBM) for the electric field integral equation (EFIE) using the boundary element method was developed, based on a simplified a posteriori error estimator for the greedy-based snapshot selection. In this paper, we extend this work and propose a certified RBM for the EFIE based on a mathematically rigorous a posteriori estimator. A central difficulty of the certified method is that the intrinsic solution space of the EFIE is \({\mathbf{H}^{-1/2}_{\text{div}}(\Gamma)}\), inducing a relatively complicated norm. Since the measured error consists of the difference between the reduced basis solution and the boundary element solution, which is a member of the discrete boundary element space, we clarify that the intrinsic norm can be replaced by an alternative norm and in this work use the \(\mathbf{H}\)(div)-norm, which is computable and demonstrated to not degrade the quality of the error estimator. A successive constraint method (SCM) for complex matrices is discussed in detail, and numerical tests for the SCM and then the certified RBM confirm the analysis.