It is proven that fluorinated gases (F-gases) have a vast impact on climate change due to their high global warming potential. Hence, it is imperative to search for new molecules to replace them in current applications, as well as technologies to capture, recover, and recycle F-gases to avoid their emissions to the atmosphere. One of the attractive technologies for this purpose is to absorb them in fluorinated ionic liquids (FILs), given their solubilization power. However, the complexity of FILs and the time-consuming experimental methodologies to fully characterize them hinder their prompt usage in this urgent field. In this work, the soft-Statistical Associating Fluid Theory (soft-SAFT) Equation of State is used as a tool to investigate the solubility of six different F-gases (R-32, R-125, R-134a, R-14, R-116, R-218) in five FILs ([C2C1Im][C4F9SO3], [C2C1Im][C4F9CO2], [C2C1py][C4F9SO3], [C2(C6F13)C1Im][N(CF3SO2)2], and [C2(C6F13)C1Im][N(C2F5SO2)2]). The robustness of the soft-SAFT approach allowed the establishment of new FIL models in a simple and fast way, and the calculation of F-gases solubility in them, in excellent agreement with existing experimental data. Once the models were assessed, a systematic study was performed regarding the structural features of FILs favoring their performance to absorb F-gases by using the soft-SAFT approach as a screening tool. It has been obtained that the solubility is favored by the presence of a perfluoroalkyl chain in the imidazolium cation, together with a bulkier anion. In all cases, [C2(C6F13)C1Im][N(C2F5SO2)2] shows a superior solubility of F-gases than the [C2(C6F13)C1Im][N(CF3SO2)2], also indicating that the addition of one carbon to the two anionic symmetric fluorinated chains contributes to the gas-philicity of the FILs. This work proves the relevance of using the soft-SAFT framework to obtain insights into the behavior of such complex systems and key trends, even when experimental data are scarce, as a step forward in assessing systems for separating and recovering F-gases.