  We consider time-harmonic Maxwell's equations set in an heterogeneous medium
with perfectly conducting boundary conditions. Given a divergence-free
right-hand side lying in $L^2$, we provide a frequency-explicit approximability
estimate measuring the difference between the corresponding solution and its
best approximation by high-order N\'ed\'elec finite elements. Such an
approximability estimate is crucial in both the a priori and a posteriori error
analysis of finite element discretizations of Maxwell's equations, but the
derivation is not trivial. Indeed, it is hard to take advantage of high-order
polynomials given that the right-hand side only exhibits $L^2$ regularity. We
proceed in line with previously obtained results for the simpler setting of the
scalar Helmholtz equation, and propose a regularity splitting of the solution.
In turn, this splitting yields sharp approximability estimates generalizing
known results for the scalar Helmoltz equation and showing the interest of
high-order methods.
