Previous studies have revealed a population of galaxies in galaxy clusters with ram pressure stripped (RPS) tails of gas and embedded young stars. We observed 1.4 GHz continuum and HI emission with the Very Large Array in its B-configuration in two fields of the Coma cluster to study the radio properties of RPS galaxies. The best continuum sensitivities in the two fields are 6 and 8 $\mu$Jy per 4'' beam respectively, which are 4 and 3 times deeper than those previously published. Radio continuum tails are found in 10 (8 are new) out of 20 RPS galaxies, unambiguously revealing the presence of relativistic electrons and magnetic fields in the stripped tails. Our results also hint that the tail has a steeper spectrum than the galaxy. The 1.4 GHz continuum in the tails is enhanced relative to their H$\alpha$ emission by a factor of $\sim$7 compared to the main bodies of the RPS galaxies. The 1.4 GHz continuum of the RPS galaxies is also enhanced relative to their IR emission by a factor of $\sim$2 compared to star-forming galaxies. The enhancement is likely related to ram pressure and turbulence in the tail. We furthermore present HI detections in three RPS galaxies and upper limits for the other RPS galaxies. The cold gas in D100's stripped tail is dominated by molecular gas, which is likely a consequence of the high ambient pressure. No evidence of radio emission associated with ultra-diffuse galaxies is found in our data.