In this work, an original procedure, based on the finite element method, is presented for the design of a Levitron©, a device made of permanent magnets and relying on stable gyroscopic magnetic levitation, using secondhand components. A perturbation force analysis is performed on finite element models of available magnets in order to derive the locus of stable equilibrium, as well as the top mass, for a given configuration of the magnets. We investigate three methods for the estimation of forces from finite element computations, two of them based on the Virtual Work principle, and one performing numerical integration of the classical expression of forces between magnets. Results are employed to realize a Levitron© in laboratory, and are shown to be in better agreement with experience than those from a simple analytical model available in the literature.