Quasi-elastic neutron scattering (QENS) and molecular dynamics (MD) simulations are applied in combination to investigate the dynamics of methane in H-ZSM-5 zeolite catalysts used for methanol-to-hydrocarbons reactions. Methane is employed as an inert model for the methanol reaction feedstock, and studies are made of the fresh catalyst and used catalysts with varying levels of coke buildup to investigate the effect of coking on reactant mobility. Measurements are made in the temperature range from 5 to 373 K. Methane mobility under these conditions is found to be extremely high in fresh ZSM-5, with the majority of movements occurring too fast to be resolved by the QENS instrument used. A small fraction of molecules undergoing jump diffusion on QENS time scales is identified and found to correspond with short-range jump diffusion within single zeolite pores as identified in MD simulations. Agreement between QENS and MD mobility measurements is found to be within 50%, validating the simulation approach employed. Methane diffusion is found to be minimally affected by moderate levels of coke buildup, while highly coked samples result in the confinement of methane to single pores within the zeolite with minimal long-range diffusion.