The research is devoted to the analytical study of the dynamics of a non-deformable conducting solid body in a contactless electromagnetic suspension. Using the mathematical apparatus of perturbation theory, the stability regions of the stationary levitation mode are determined, and the features of nonlinear oscillations are investigated. Various approaches to accounting for induction currents in a solid body within the coupled electromechanical model are considered. In the context of the development of high-precision micromechanical sensors, the analytical estimates of the effective quasi-zero stiffness of the contactless suspension are compared with known experimental data.