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 \times 10 ^ { 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 } .