  We report on Green Bank Telescope 23.87 GHz NH$_3$(3,3), emission
observations in five supernova remnants interacting with molecular clouds
(G1.4$-$0.1, IC443, W44, W51C, and G5.7$-$0.0). The observations show a clumpy
gas density distribution, and in most cases the narrow line widths of
$\sim3-4$\,km\,s$^{-1}$ are suggestive of maser emission. Very Large Array
observations reveal 36~GHz and/or 44~GHz CH$_3$OH, maser emission in a majority
(72\%) of the NH$_3$, peak positions towards three of these SNRs. This good
positional correlation is in agreement with the high densities required for the
excitation of each line. Through these observations we have shown that
CH$_3$OH, and NH$_3$, maser emission can be used as indicators of high density
clumps of gas shocked by supernova remnants, and provide density estimates
thereof. Modeling of the optical depth of the NH$_3$(3,3) emission is compared
to that of CH$_3$OH, constraining the densities of the clumps to a typical
density of the order of $10^5$~cm$^{-3}$ for cospatial masers. Regions of gas
with this density are found to exist in the post-shocked gas quite close to the
SNR shock front, and may be associated with sites where cosmic rays produce
gamma-ray emission via neutral pion decay.
