  We consider a linearised inverse conductivity problem for electromagnetic
waves in a three dimensional bounded domain at a high time-harmonic frequency.
Increasing stability bounds for the conductivity coefficient in the full
Maxwell system and in a simplified transverse electric mode are derived. These
bounds contain a Lipschitz term with a factor growing polynomially in terms of
the frequency, a Holder term, and a logarithmic term which decays with respect
to the frequency as a power. To validate this increasing stability numerically,
we propose a reconstruction algorithm aiming at the recovery of sufficiently
many Fourier modes of the conductivity. A numerical evidence sheds light on the
influence of the growing frequency and confirms the improved resolution at
higher frequencies.
