Two families of parametrized mixed variational principles for linear electromagnetody-namics are constructed. The first family is applicable when the current density distribution is known a priori. Its six independent fields are magnetic intensity and flux density, magnetic potential, electric intensity and flux density and electric potential. Through appropriate spe-cialization of parameters the first principle reduces to more conventional principles proposed in the literature. The second family is appropriate when the current density distribution and a conjugate Lagrange multiplier field are adjoined, giving a total of eight independently varied fields. In this case it is shown that a conventional variational principle exists only in the time-independent (static) case. Several static functionais with reduced number of varied fields are presented. The application of one of these principles to construct finite elements with current prediction capabilities is illustrated with a numerical example.