We present a modeling technique that combines a statistical-mechanical coarse-graining scheme with a nonequilibrium molecular simulation algorithm to provide an efficient simulation of steady-state permeation across a microporous material. The coarse-graining scheme is based on the mapping of an atomistic model to a lattice using multidimensional free-energy and transition-state calculations. The nonequilibrium simulation algorithm is a stochastic, lattice version of the recently developed atomistic dual-control-volume grand canonical molecular dynamics. We demonstrate the approach on a model of methane permeating through a bulk portion of siliceous zeolite ZK4 at 300 K under imposed fugacity differences. We predict the coarse-grained (cage-level) density profiles and observe the development of nonlinearities as the magnitude of the fugacity difference is increased. From the net flux of methane we also predict a mean permeability coefficient under the various conditions. The simulation results are obtained over time scales on the order of microseconds and length scales on the order of dozens of nanometers. (C) 2004 American Institute of Physics.