This paper explores the discontinuous Galerkin (DG) methods for solving the Vlasov–Maxwell (VM) system, a fundamental model for collisionless magnetized plasma. The DG method provides an accurate numerical description with conservation and stability properties. This work studies the applicability of a post-processing technique to the DG solution in order to enhance its accuracy and resolution for the VM system. In particular, superconvergence in the negative-order norm for the probability distribution function and the electromagnetic fields is established for the DG solution. Numerical tests including Landau damping, two-stream instability, and streaming Weibel instabilities are considered showing the performance of the post-processor.