The quantum chemical COSMO-RS method was applied to describe supported ionic liquid membranes (SILMs) with an enhanced capacity of selective separation of CO2 from N-2, in order to contribute to the design of CO2 postcombustion capture technologies based on ionic liquid (IL) solvents. First, the predictive capability of the COSMO-RS method was evaluated through a comparison with a wide range of selectivity experimental data, and a further optimization based on the Henry's Law constant of each solute in ILs was developed to improve the prediction of CO2/N-2 selectivity in SILMs. Afterward, the optimized COSMO-RS approach was applied to design suitable SILM systems for CO2/N-2 separation by driving a computational screening of 224 ILs, with results illustrating the capability of [SCN-]-based ILs to enhance the selective separation of CO2 from N-2. Finally, to better understand SILM behavior in CO2 separation, the CO2/N-2 selectivity differences among ILs were successfully related to the excess enthalpy of CO2-IL and N-2-IL mixtures in solution predicted by COSMO-RS. In addition, the intermolecular interactions (electrostatic, hydrogen bonding, and van der Waals) between CO2-IL and N-2-IL systems in the liquid phase, quantified by COSMO-RS, were analyzed in order to contribute to the rational selection of SILMs with positive characteristics for CO2/N-2 selective separation.