  We consider residual-based a posteriori error estimators for Galerkin-type
discretizations of time-harmonic Maxwell's equations. We focus on
configurations where the frequency is high, or close to a resonance frequency,
and derive reliability and efficiency estimates. In contrast to previous
related works, our estimates are frequency-explicit. In particular, our key
contribution is to show that even if the constants appearing in the reliability
and efficiency estimates may blow up on coarse meshes, they become independent
of the frequency for sufficiently refined meshes. Such results were previously
known for the Helmholtz equation describing scalar wave propagation problems
and we show that they naturally extend, at the price of many technicalities in
the proofs, to Maxwell's equations. Our mathematical analysis is performed in
the 3D case, and covers conforming N\'ed\'elec discretizations of the first and
second family, as well as first-order (and hybridizable) discontinuous Galerkin
schemes. We also present numerical experiments in the 2D case, where Maxwell's
equations are discretized with N\'ed\'elec elements of the first family. These
illustrating examples perfectly fit our key theoretical findings, and suggest
that our estimates are sharp.
