Polarimetry, a powerful diagnostic tool, can provide information on the density and magnetic field, utilizing the Faraday and the Cotton–Mouton effects in a magnetized plasma. Both effects contribute to the change of the polarization of an electromagnetic wave traversing a magnetized plasma such that, unless both effects are small, the measurable output polarization does not provide the 'pure' effects in terms of Faraday rotation angle and Cotton–Mouton phase shift angle, which are directly related to simple line-of-sight integrals of the electron density times certain components of the magnetic field. In view of the importance of the latter, a new formalism has been developed, which delivers narrow limits to these quantities in terms of analytic formulae that contain nothing but the input and output polarization parameters. The approach is valid for vertical lines of sight in toroidal devices whose toroidal field dominates over other field components perpendicular to the line of sight. Examples relating to measurements at JET demonstrate the capabilities of the method.