We have identified conditions in which the atomic force microscope can be used to stretch a meniscus of a perfluoropolyether (PFPE) lubricant pinned between an AFM tip and a nanometer-thick PFPE film to obtain the disjoining pressure of the film. Under quasi-equilibrium conditions, the chemical potential of the film can be equated to that of the stretched meniscus. A theory is presented that provides a complete description of the capillary force of a stretched meniscus. Fits of the theory to quasi-equilibrium force-extension curves yield the effective meniscus curvature and, by extension, the disjoining pressure of the underlying film. AFM force curves collected at varying film thicknesses compare very well with predictions from Lifshitz theory of dispersive interactions in thin films, with no adjustable parameters. This complete description of meniscus deformation during atomic force microscopy force-extension experiments makes possible the measurement of unknown disjoining pressures as required for screening of lubricant-overcoat combinations required for next-generation data storage systems.