  We discuss a Steklov-type problem for Maxwell's equations which is related to
an interior Calder\'{o}n operator and an appropriate Dirichlet-to-Neumann type
map. The corresponding Neumann-to-Dirichlet map turns out to be compact and
this provides a Fourier basis of Steklov eigenfunctions for the associated
energy spaces. With an approach similar to that developed by Auchmuty for the
Laplace operator, we provide natural spectral representations for the
appropriate trace spaces, for the Calder\'{o}n operator itself and for the
solutions of the corresponding boundary value problems subject to electric or
magnetic boundary conditions on a cavity.
