  We have used the VLBI High Sensitivity Array (VLBA with VLA, Green Bank
Telescope, and Arecibo) to search for young radio supernovae in three nearby
Wolf Rayet dwarf galaxies containing Super Star Clusters (SSCs) and signs of
extreme star formation in the last few million years. No milliarcsecond radio
sources were detected in II Zw 40, He 2-10, or NGC 5253, implying that these
galaxies contain few radio supernovae, despite the fact that they have at least
some star formation going back to 10 million years ago. The upper limits of the
source powers range from 6 x 10^17 W/Hz to ~2 x 10^18 W/Hz at 5 GHz, roughly
0.6 to 2.2 times the power of the galactic supernova remnant Cassiopeia A.
Comparison with the radio supernova population in Arp 299 implies that the
current supernova rates in the three dwarf galaxies are below 10^{-2}/yr,
consistent with standard star formation models that predict supernova rates of
10^{-3}/yr or less in our targets. In He 2-10, the VLBI non-detection of a
compact VLA source with a significant nonthermal component indicates that this
source may be dominated by one or more supernova remnants with ages of a few
hundred years or more, which are comparable to Cas~A in power, and size.
