To date, the design of advanced separation processes, such as the extractive distillation with ionic liquids (ILs), for the separation of common close-boiling refrigerant blends relies almost exclusively on binary equilibrium data obtained for single-gas/solvent systems, thus neglecting the influence of possible mixture effects. In this work, Nuclear Magnetic Resonance (NMR) spectroscopy and pulsed gradient spin echo (PGSE) NMR are proposed for the sequential assessment of the single and mixed-gas vapor-liquid equilibrium and self-diffusivity of two fluorinated refrigerants, difluoromethane (R-32) and pentafluoroethane (R-125), in the IL 1-ethyl-3-methylimidazolium dicyanamide at 303.1 K and pressures up to 4 bar, either as pure R-32 or using the commercial refrigerant blend R-410A. The results confirmed that the mixed-gas solubility and self-diffusivities were essentially equal to those obtained with pure feed gas, thus significant mixing effects were not observed for this particular system. However, an increase in the self-diffusion coefficients was observed with the concentration of absorbed gas, which was more significant for the smallest hydrofluorocarbon (R-32) than for R-125. This technique also allowed evaluating the mobility of the IL moieties, which was slightly higher for the IL anion. Moreover, the self-diffusion coefficients of the IL ions also increased with the amount of gas absorbed, yet less markedly than for the refrigerants. Overall, the NMR technique proved to be an accurate method for the rapid screening of possible mixture effects in equilibrium and transport properties of refrigerant and IL systems, thus providing essential information for designing novel advanced separation processes.