We investigate the diagnostic potential of polarimetric measurements with filtergraph instruments. Numerical simulations are used to explore the possibility of inferring the magnetic field vector, its filling factor, and the thermodynamics of model atmospheres when only a few wavelength measurements are available. These simulations assume the magnetic Sun to be represented by Milne–Eddington atmospheres. The results indicate that two wavelength measurements are insufficient to reliably determine the magnetic parameters, regardless of whether magnetograph techniques or least-squares fitting inversions are used. However, as few as four measurements analyzed with the inversion technique provide enough information to retrieve the intrinsic magnetic field with an accuracy better than 10% in most cases.