A method to determine Joule-Thomson inversion curves, using isobaric-isothermal Monte Carlo molecular simulations, is presented. Volumetric data obtained through the simulations is interpreted by means of thermodynamic relations to obtain the locus of points in which the isenthalpic derivative of temperature with respect to pressure vanishes. The procedure is exemplified for a Lennard-Jones fluid and the low-temperature branch of the inversion curve is obtained. In general, Joule-Thomson inversion curves obtained by molecular simulation may be used either as an unambiguous test for equations of state in the supercritical and high-pressure regions or for the prediction of real fluid behavior, should the potential be well known. Examples of both applications are presented.