  We hereby report on a sensitive search for radio continuum observations from
a sample of 34 Mira and semi-regular variable stars. The main aim of this
survey was to search for thermal free-free emission from post-shock ionised
gas. Thirty-four stars were observed at 3- and 6-cm using the Australia
Telescope Compact Array. Radio continuum emission was detected from one source
only, the symbiotic Mira R Aqr. No continuum emission was detected from the
other sources, with three-sigma upper limits of typically 0.3 mJy. From the
upper limits to the radio flux densities, we have found upper limits to the gas
brightness temperatures near two stellar radii at a characteristic size of
$5\times10^{13}$ cm. Upper limits to shock velocities have been estimated using
a shock model. For the 11 nearest sources in our sample we obtain brightness
temperatures below 6 000 K and shock velocities below 13 km s$^{-1}$. For 11
out of 14 sources with previously published detections, the radio brightness
temperatures are below 4 000 K. For an upper limit of 4 000 K, we estimate that
the shock velocities at two stellar radii are below 10 km s$^{-1}$.
