We present experimental and theoretical results for single-component permeance of CH4 and CF4 through a supported silicalite membrane at a range of temperatures and pressures. Our theoretical model uses a continuum description of molecular transport through zeolite crystals that is directly parametrized from atomically detailed simulations of molecular adsorption and transport. This approach does not require any assumptions regarding the loading dependence of the adsorbed species' transport or Maxwell-Stefan diffusivities. Our results are the first direct comparison between a fully atomistic description of intracrystalline transport and permeance measurements for a macroscopic zeolite membrane. These results help to isolate the contributions to the overall flux through polycrystalline zeolite membranes that arise from molecular transport through nonzeolitic pores. We also discuss avenues for future extensions and improvements of our atomistic approach to modeling practical zeolite membranes.