A combination of a pressure-controlled scanning calorimetry (PCSC) and Monte Carlo simulations (MCS) is presented for an unequivocal determination of the Joule-Thomson inversion curve (JTIC) with high accuracy over wide ranges of pressure and temperature. The MCS performed with the fluctuation method are fast and easy to operate, but the results can vary significantly depend on the set of primary molecular data needed for the calculations. The PCSC is an experimental and more laborious technique, but supplies data of high quality. Thus, it can be used to check the MCS data and to verify the molecular parameters used for the calculations. Such a combined procedure was used in the present study for determination of the JTIC for methane, for which a correlation equation was established valid from 302.9 to 586.5 K. A combination of a direct experimental technique with molecular simulations permits also to better understand the complex behavior of the Joule-Thomson inversion phenomenon over wide ranges of pressure and temperature.