We have studied the behavior of confined ultrathin films of a simple model system in which the fluid and wall particles were modeled as Lennard-Jones rare gas atoms by Monte Carlo simulations. We have used a new (Grand isoforce) statistical ensemble in these simulations, with which it is possible to simulate thin films under constraints (fixed chemical potential mu, temperature T, stress tensor components T-zz, T-xz, and T-yz) that are presumably resembling the conditions under which the Surface Force Apparatus (SFA) operates. We also employ another ensemble, with fixed (mu, T, V, T-xz, T-yz), which we call "Grand Isoshear." Some important features of the SFA experiments on globular, nonpolar, molecular liquids have been reproduced in the simulations. Using the new statistical ensembles we have shown that a periodic solvation force can be obtained under the operating conditions of the SFA, although some additional features may exist, but remain hidden in the experiments if located in the unstable branch of the solvation force curve. We demonstrate that epitaxy between the solid walls and the fluid molecules is not required to obtain an apparently periodic solvation force curve.