Four novel sulfur-containing polymers of intrinsic microporosity (PIMs) were evaluated for use in CO2/CH4 gas separation membranes by means of predictive molecular simulations. It was found that the introduction of sulfur into the monomer backbone provides an extra, less shape-persistent site of contortion, which results in a less porous polymer framework. However, the CO2 adsorption isotherms and isosteric heats of adsorption were greatly, increased in sulfonyl-functionalized PIMs. In addition; the 1:1 mixed-gas adsorption selectivity values of sulfonyl PIMs were shown to be enhanced by the highly polar functionality, which was calculated to be 23 at atmospheric pressure, and 50 for the lowest pressures reported. The mixed-gas adsorption selectivity is shown to be exponentially related to the difference between the isosteric heats of adsorption of CO2 and CH4 normalized by the total void space (Delta q(st)/phi), which is referred to as the adsorbility. The results presented in this work. should. facilitate the purposeful design and screening of new intrinsically microporous polymer membranes with increased CO2/CH4 gas separation performance.