We summarize the development and application of an important class of discrete differential operators for structured and unstructured grids. Mimetic differencing operators are derived from discrete approximations of adjoint equations governing the continuous operators and hence inherit important symmetry preserving properties. We demonstrate a scheme which represents problems in electromagnetics with discontinuous material parameters using only continuous variables and the derivation of the appropriate operators. The complete set of operators for divergence, gradient and curl are currently being added to the PDEUM software framework.