The paper presents for the first time results of very large amplitude squeeze-film damping simulations in MEMS devices, using the different level models: 3D numerical solution of Navier-Stokes equations (using CFD-ACE+ from CFDRC), and compact/behavioral models (in Spice and Saber-MAST formats). The results of the compact model, based on nonlinear RL equivalent circuit, agree very well with the 3D results even for very large amplitudes of plate motion, accompanied by significant changes of pressure. For the amplitudes reaching 90% of the nominal gap height between plates, the relative pressure change due to squeeze forces is 10 to 15 times bigger than static ambient pressure. The Saber-MAST version of the model uses directly mechanical quantities: position as input (across variable) and damping force as output (through variable), which is compatible with hierarchical representation for system-level design of MEMS.