  We propose a novel a posteriori error estimator for the N\'ed\'elec finite
element discretization of time-harmonic Maxwell's equations. After the
approximation of the electric field is computed, we propose a fully localized
algorithm to reconstruct approximations to the electric displacement and the
magnetic field, with such approximations respectively fulfilling suitable
divergence and curl constraints. These reconstructed fields are in turn used to
construct an a posteriori error estimator which is shown to be reliable and
efficient. Specifically, the estimator controls the error from above up to a
constant that tends to one as the mesh is refined and/or the polynomial degree
is increased, and from below up to constant independent of $p$. Both bounds are
also fully-robust in the low-frequency regime. The properties of the proposed
estimator are illustrated on a set of numerical examples.
