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This paper deals with the problem of accurate evaluation of global quantities related to the electrostatic fields in micro-electro-mechanical systems (MEMS). In particular, the capacitance and the electrostatic force play often an important role in the design of micro-machines. In spite of the fact that some simplified formulas have been proposed so far, in many cases it is necessary to improve the accuracy of computations. This paper intends to provide some new investigations on the numerical evaluations of electrostatic quantities by means of the finite element method (FEM), presenting some numerical results on realistic examples and comparing them to experimental outcomes.