We discuss the application of Monte Carlo methods to the self-consistent calculation of a Ginzburg-Landau free energy functional for Lennard-Jones systems in three dimensions. Following this discussion, we demonstrate that the parameters in the coarse-grained free energy can be extracted from a multivariate distribution of energies and particle densities which, when suitably reweighted, permit one to extrapolate the results to other nearby points in the thermodynamic parameter space. For the purposes of illustration, both single-phase and liquid-gas coexistence are considered here with the aim of describing various regions of the phase diagram with a single function and, in doing so, providing a link between atomistic and mesoscopic length scales.