The aim of this paper is to demonstrate robust parameter extraction from the frequency response of MEMS devices exhibiting pronounced nonlinearities. We describe a general methodology, based on parameter extraction from nonlinear large-signal frequency response, whose accuracy appears to be limited in practice only by noise and by the mathematical model of the structure under consideration. We illustrate this by two complete case studies of capacitive MEMS resonators driven to large-amplitude regimes. Theoretical analysis, simulations and experimental measurements strongly support our conclusions.