  We address the problem of coupling non-Hermitian systems, treated as
fundamental rather than effective theories, to the electromagnetic field. In
such theories the observables are not the $\bs{x}$ and $\bs{p}$ appearing in
the Hamiltonian, but quantities $\bs{X}$ and $\bs{P}$ constructed by means of
the metric operator. Following the analogous procedure of gauging a global
symmetry in Hermitian quantum mechanics we find that the corresponding gauge
transformation in $\bs{X}$ implies minimal substitution in the form $\bs{P}\to
\bs{P} - e\bs{A}(\bs{X})$. We discuss how the relevant matrix elements
governing electromagnetic transitions may be calculated in the special case of
the Swanson Hamiltonian, where the equivalent Hermitian Hamiltonian $h$ is
local, and in the more generic example of the imaginary cubic interaction,
where $H$ is local but $h$ is not.
