We present Very Large Array (VLA) radio continuum and Infrared Astronomy Satellite (IRAS) far-infrared (FIR) observations of 16 low luminosity galaxies of mostly low surface brightness. All galaxies had previously claimed single dish radio continuum detections. However, at the frequencies of our observations (1.49 and 8.48 GHz), we find significant radio emission for two objects only. We show that the other previously claimed detections are due to confusion with physically unrelated background sources. This implies a low radio continuum detection rate for these galaxies. Re-reduced IRAS scans yield significant far-infrared flux densities in at least one IRAS band for 6 of the 16 galaxies. These, together with the FIR and radio continuum upper limits, are consistent with the well established radio/FIR relation, where most of our galaxies populate the low-luminosity end. From the radio continuum and FIR flux densities and their upper limits we estimate the current star formation rates and demonstrate that the galaxies are currently passive in forming stars, in agreement with previous optical investigations. There is an indication that the galaxies were forming stars more intensively averaged over their lifetime than they are presently.