Hierarchical matrices, or H-matrices are an error-controllable framework that permit efficient inversion and decomposition of matrices arising in time-harmonic electromagnetics applications. This work evaluates the capabilities of H-matrices for preconditioning iterative solutions to the time-harmonic discontinuous Galerkin method. Particular focus is given to exact radiating boundary conditions in the discontinuous Galerkin formulation. In order to ensure a deep understanding of H-matrix theory and operations, an H-matrix framework has been developed. Performance of H-LU decompositions as error-controllable preconditioners is demonstrated, showing the desired time, memory, and accuracy scaling.