Since their discovery, deep eutectic solvents (DES) have been explored in multiple applications. However, the complete physicochemical characterization is still nonexistent for many of the proposed and used DES. In particular, vapor pressure, which is a crucial property for the application of DES as solvents, is very rarely available. In this work, the measurement of the total and partial pressures of two sulfolane-based DES, tetrabutylammonium bromide:sulfolane and tetrabutylphosphonium bromide:sulfolane, in several proportions, from 40 to 100 degrees C and atmospheric pressure, was performed using headspace gas chromatography mass spectrometry, HS-GC-MS. A large decrease on the total pressure was recorded which, together with the finding that total pressures showed negative deviations from Raoult's law, is indicative of the favorable, strong interactions between the two components within the DES. Additionally, the study of vapor pressure change with DES molar composition was carried out, and surprisingly, the existence of inflection points in the pressure curve was observed. Experimental results were modeled using the PC-SAFT equation of state, and in addition, MD simulations were performed to provide a molecular understanding of the pressure data. Considering the different results and insights obtained from the used strategies, it can be concluded that both DES systems have especially strong interactions between salt and sulfolane, at high sulfolane content, due to the different structural rearrangement of the liquid state.