We present a new generalized Ramo-Shockley theorem (GRST) to evaluate contact currents, applicable to classical moment-based simulation techniques, as well as semiclassical Monte Carlo and quantum mechanical transport simulation, which remains valid for inhomogeneous media, explicitly accounts for generation/recombination processes, and clearly distinguishes between electron, hole, and displacement current contributions to contact current. We then show how this formalism may be applied to Monte Carlo simulation to obtain equations for minimum-variance estimators of steady-state contact current, making use of information gathered from all particles within the device. Finally, by means of an example, we demonstrate this technique’s performance in acceleration of convergence time.