Aiming at designing ionic liquids for the purification of natural gas, the solubility of methane in ionic liquids is investigated here through the measurement of the solubilities of methane in four ionic liquids (ILs), in a wide range of molar fractions, temperature and pressures. With the exception of the phosphonium-based IL, which behaves as an almost ideal solution, the other ionic liquids show strong positive deviations from ideality, resulting from non-favorable interactions between CH4 and the ILs. The results indicate that the non-ideality of the solution increases, and the solubility decreases, with the polarity of the ionic liquid. The effect of the ionic liquid polarity on the CO2/CH4 and H2S/CH4 selectivities is evaluated here. The ionic liquids studied here present the largest CO2/CH4 and H2S/CH4 selectivities ever reported. The selectivity models previously proposed in the literature are tested against these new experimental data and are shown to fail. Furthermore, it is shown that describing the ILs' polarity using the Kamlet-Taft parameters, the CO2/CH4 and H2S/CH4 selectivities correlate well with the [small beta]-parameter providing a key to the design of ionic liquids with enhanced selectivities.