We report on the operational principle, modeling, fabrication and characterization of an electrostatically actuated force/acceleration sensor with mechanically nonlinear stiffening suspension. The suspension incorporates initially curved beams oriented in such a way that both the electrostatic and inertial forces applied to the beam's ends are directed predominantly along the beam. Since the stiffness of the curved beam is significantly lower than that of the straightened beam, the force-displacement dependence of the suspension is of the self-limiting type while the suspension itself serves as a compliant constraint. Application of a softening electrostatic force, provided by a parallel-plate transducer, results in pull-in instability followed by the steep increase in the suspension stiffness and the appearance of an additional stable configuration of the device. In accordance with the model results the dependence between the acceleration and the shift of the pull-in voltage induced by the acceleration is nearly linear and the pull-in voltage monitoring can be used for the measurement of the acceleration. Model results show that using the suggested approach significantly improves device resolution, extends dynamic range, and improves reliability by eliminating contact. Devices of several configurations were fabricated from a silicon on insulator (SOI) substrate using a deep reactive ion etching (DRIE) based process. Preliminary experimental results imply that the suggested approach is feasible.