A general closed expression is derived in the frequency domain for the minimum free energy, related to a state of a linear electromagnetic conductor with memory effects in the constitutive equation of the current density, by evaluating the maximum recoverable work obtainable from the given state. The constitutive equation with memory is given by a linear relation between the current density and the electric field, expressed by a linear functional of the history of this field and a term proportional to its actual value. Another equivalent formulation is also given and used to derive explicit formulae for the particular case of a discrete spectrum model.