  In this paper we consider a numerical homogenization technique for
curl-curl-problems that is based on the framework of the Localized Orthogonal
Decomposition and which was proposed in [D. Gallistl, P. Henning, B.
Verf\"urth. SIAM J. Numer. Anal. 56-3:1570-1596, 2018] for problems with
essential boundary conditions. The findings of the aforementioned work
establish quantitative homogenization results for the time-harmonic Maxwell's
equations that hold beyond assumptions of periodicity, however, a practical
realization of the approach was left open. In this paper, we transfer the
findings from essential boundary conditions to natural boundary conditions and
we demonstrate that the approach yields a computable numerical method. We also
investigate how boundary values of the source term can effect the computational
complexity and accuracy. Our findings will be supported by various numerical
experiments, both in $2D$ and $3D$.
