Previously, we found that the ionic liquid (IL) 1-ethyl-3 methylimidazolium tris(pentafluoroethyl)trifluorophosphate ([emim][FAP]) shows the highest carbon dioxide (CO2) solubility of all ILs studied so far. Therefore, this IL is a very interesting solvent for gas separations, such as the removal of CO2 from sour gas, as long as the solubility of methane (CH4) in the same IL is sufficiently low. In this work, we present new experimental measurements of the CH4 solubility in [emim][FAP]. This solubility has been determined by measuring the bubble point pressures for CH4 concentrations ranging from (5.2 to 15.5) mol % and within a temperature range of (293.30 to 363.42 K) using a synthetic method. The solubilities of CH4 in [emim][FAP] are compared to the CH4 solubilities in other ILs. This comparison shows that the solubility of CH4 in the various ILs slightly decreases in the order: [hmim][Tf2N] > [emim][FAP] > [bmim][Tf2N]. The solubilities of CH4 in various ILs are compared with CO2 solubilities in the same ILs, showing the much lower solubility of CH4 in all ILs studied. The high solubility of CO2 compared to CH4 in [emim][FAP] indicates the possibility of using this IL in separating CO2 from natural gas. The obtained selectivity for this separation at a temperature of 333.15 K is S = HCH4/HCO2 = 7.74, which is similar to CO2/CH4 separation ratios in other ILs (e.g., S = 8.26 for [bmim][Tf2N] and S = 6.10 for [hmim][Tf2N]).