The microscopic structure of molecularly thin fluid films confined between solid substrates with macroscopically curved surfaces is investigated by means of grand canonical ensemble Monte Carlo (GCEMC) simulations, in which the thermodynamic state of the film is determined by its chemical potential mu and temperature T. This situation is akin to experiments involving the surface forces apparatus (SFA) in which the film is confined between two crossed cylinders of macroscopic radius R. The key quantity measured directly in SFA experiments is the "force per radius R," F(h)/R, exerted by the film on the curved surfaces. This ''solvation force'' can be related to the local stress T-zz(h) normal to the locally planar surfaces, where h is the shortest:distance between them. Because T-zz(h) and the microscopic structure of the confined film can be computed by GCEMC, the relation between T-zz and the macroscopically defined quantity F/R can be employed to interpret the dependence of the latter in terms of variations of the film's local microscopic structure with h. For a liquid-crystalline film it is shown that reorientational effects are distinctly manifest in T-zz(h) but are reflected only weakly in F(h)/R and are therefore likely to be missed if the interpretation of SFA experiments is based solely upon the latter. Pseudo-experimental F(h)/R curves generated by GCEMC for a nematic liquid-crystalline film are in qualitative agreement with recent SFA data [M. Ruths, S. Steinberg, and J. N. Israelachvili, Langmuir 12, 6637 (1996)], which suggests that one may gain deeper insight into the microscopic structure of confined films through a decomposition of experimentally determined solvation forces F(h)/R into T-zz(h) by inverting the integral relation linking the two.