  We report for the first time the detection of thermal free-free emission from
post-flare loops at 34GHz in images from the Nobeyama Radioheliograph (NoRH).
We studied 8 loops, 7 of which were from regions with extremely strong coronal
magnetic field reported by Fedenev et al. (2023). Loop emission was observed in
a wide range of wavelength bands, up to soft X-rays, confirming their
multi-temperature structure and was associated with noise storm emission in
metric wavelengths. The comparison of the 17GHz emission with that at 34GHz,
after a calibration correction of the latter, showed that the emission was
optically thin at both frequencies. We describe the structure and evolution of
the loops and we computed their density, obtaining values for the top of the
loops between 1 and 6 x 10^10 cm^-3, noticeably varying from one loop to
another and in the course of the evolution of the same loop system; these
values have only a weak dependence on the assumed temperature, 2 x 10^6 K in
our case, as we are in the optically thin regime. Our density values are above
those reported from EUV observations, which go up to about 10^10 cm^-3. This
difference could be due to the fact that different emitting regions are sampled
in the two domains and/or due to the more accurate diagnostics in the radio
range, which do not suffer from inherent uncertainties arising from abundances
and non-LTE excitation/ionization equilibria. We also estimated the magnetic
field in the loop tops to be in the range of 10 to 30G.
