An approach based on proper orthogonal decomposition and Galerkin projection is presented for developing low-order nonlinear models of the gas film pressure within mechanical gas face seals. A technique is developed for determining an optimal set of global basis functions for the pressure field using data measured experimentally or obtained numerically from simulations of the seal motion. The reduced-order gas film models are shown to be computationally efficient compared to full-order models developed using the conventional semidiscretization methods. An example of a coned mechanical gas face seal in a flexibly mounted stator configuration is presented. Axial and tilt modes of stator motion are modeled, and simulation studies are conducted using different initial conditions and force inputs. The reduced-order models are shown to be applicable to seals operating within a wide range of compressibility numbers, and results are provided that demonstrate the global reduced-order model is capable of predicting the nonlinear gas film forces even with large deviations from the equilibrium clearance.