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In this work, a visual high pressure sapphire cell was employed to measure the solid-fluid equilibrium (SFE) of methane + neopentane binary systems at temperatures down to 90 K and pressures up to 11 MPa. First, the conditions of solid-liquid-vapour equilibrium (SLVE) and solid-liquid equilibrium (SLE) were measured for synthetic mixtures of neopentane in methane. The SFE conditions were then investigated at a constant neopentane mole fraction of 2036 ppm. The SFE data showed a variety of phase transitions starting at higher temperatures (SVE conditions) where neopentane solid formed. Further cooling at pressures below 2 MPa resulted in a reduction of the amount of solid neopentane present, which eventually melted entirely after passing through a solid-liquid retrograde boundary. A model implemented in the software tool ThermoFAST was tuned to SFE experimental data obtained in this work and taken from the literature, which led to an optimized binary interaction parameter, capable of describing the experimental data within an R.M.S deviation of 2.7 K. Overall, the data measured suggest that neopentane is quite soluble in methane (0.10 mol fraction) at typical LNG conditions, with limited freeze-out risk during production given the small concentrations of neopentane typically present in natural gas.