Separating mixtures that form azeotropes or have relative volatilities close to 1.0 has always been a challenging problem. Conventional distillation cannot yield high purity products for these systems, so separating them often becomes a capital- and energy-intensive process. One of the most popular alternative methods used to accomplish these separations is extractive distillation, in which an entrainer is added to increase the relative volatility of the mixture. Ionic liquids (ILs) show great promise as entrainers due to their extremely low volatility, thermal stability, and chemical diversity. In this work, 1-ethyl-3-methylimidazolium methanesulfonate ([EMIM][MeSO3]) and 1-ethyl-3-methylimidazolium methylsulfate ([EMIM][MeSO4]) were investigated for their ability to break the methyl acetate + methanol azeotrope at 313.15 K. [EMIM][MeSO3] was able to break the azeotrope at just 2.5 mol % IL, the lowest value currently recorded in the literature. [EMIM][MeSO4] also performed well, breaking the azeotrope at 6.0 mol %. Finally, the Non-Random Two-Liquid (NRTL) model was used to correlate the vapor-liquid equilibrium (VLE) data of the binary systems and then predict the ternary phase behavior of systems with ionic liquids.