  This work applies the contact formalism of classical mechanics and classical
field theory, introduced by Herglotz and later developed in the context of
contact geometry, to describe electromagnetic systems with dissipation. In
particular, we study an electron in a non-perfect conductor and a variation of
the cyclotron radiation. In order to apply the contact formalism to a system
governed by the Lorentz force, it is necessary to generalize the classical
electromagnetic gauge and add a term in the Lagrangian. We also apply the
k-contact theory for classical fields to model the behaviour of electromagnetic
fields themselves under external damping. In particular, we show how the theory
describes the evolution of electromagnetic fields in media under some
circumstances. The corresponding Poynting theorem is derived. We discuss its
applicability to the Lorentz dipole model and to a highly resistive dielectric.
