We present the results of radio observations of the black hole binaries GRO J1655-40 and XTE J1550-564 in quiescence, with the upgraded Australia Telescope Compact Array. Neither system was detected. Radio flux density upper limits (3σ) of 26 μJy (at 5.5 GHz), 47 μJy (at 9 GHz) for GRO J1655-40 and 1.4 mJy (at 1.75 GHz), 27 μJy (at 5.5 GHz), 47 μJy (at 9 GHz) for XTE J1550-564 were measured. In conjunction with quasi-simultaneous Chandra X-ray observations (in the case of GRO J1655-40) and Faulkes Telescope optical observations (XTE J1550-564) we find that these systems provide the first evidence of relatively `radio-quiet' black hole binaries at low luminosities, indicating that the scatter observed in the hard state X-ray-radio correlation at higher luminosities may also extend towards quiescent levels.