This paper presents the results of adsorption and permeation experiments of hydrogen and methane at elevated temperatures on a carbon-based nanoporous membrane material provided by Fraunhofer IKTS. The adsorption of pure components was measured between 90 °C and 120°C and pressures up to 45 bar. The Langmuir adsorption isotherm shows the best fit for all data points. Compared to available adsorption isotherms of H2 and CH4 on carbon, the adsorption on the investigated nanoporous carbon structures is significantly lower. Single-component permeation experiments were conducted on membranes at temperatures up to 220 °C. After combining the experimental results with a Maxwell-Stefan surface diffusion model, Maxwell-Stefan surface diffusion coefficients Dis were calculated. The calculated values are in line with an empirical model and thus can be used in future multi-component modeling approaches in order to better analyze and design a membrane system. The published adsorption data fill a gap in the available adsorption data for CH4 and H2.