Radio observations of two isolated neutron stars, RX J0720.4-3125 and RX J0806.4-4132, have been made with the Australia Telescope Compact Array at a frequency of 1.4 GHz. No continuum emission is detected from either object with a 3σ upper limit of 0.2 mJy. The data were also folded synchronously with the known rotation periods of 8.4 and 11.4 s respectively. No pulsed emission was detected. If the pulse duty cycle is small, the upper limit on pulsed emission can be reduced still further to 0.04 mJy. The best evidence seems to indicate that the isolated neutron stars detected by the ROSAT All-Sky Survey are relatively young objects, born with a very high magnetic field.