  Context. MWC 656 is the recently discovered first binary system case composed
of a Be-type star and an accreting black hole. Its low X-ray luminosity
indicates that the system is in a quiescent X-ray state.
  Aims. The aim of our investigation is to establish if the MWC 656 system has
detectable radio emission and if the radio characteristics are consistent with
those of quiescent black hole systems.
  Methods. We used three archived VLA data sets, one hour each, at 3 GHz and
seven new VLA observations, two hours each, at 10 GHz to produce very high
sensitivity images, down to $\sim$1$\,\mu$Jy.
  Results. We detected the source twice in the new observations: in the first
VLA run, at periastron passage, with a flux density of 14.2$\,\pm\,$2.9 $\mu$Jy
and by combining all together the other six VLA runs, with a flux density of
$3.7 \pm 1.4$ $\mu$Jy. The resulting combined map of the archived observations
has the sensitivity of $1 \sigma = 6.6\, \mu Jy$ but no radio emission is there
detected.
  Conclusions. The radio and X-ray luminosities agree with the behaviour of
accreting binary black holes in the hard and quiescent state. In particular,
MWC 656 in the $L_X$, $L_R$ plane occupies the same region as A0620$-$00 and
XTE J1118+480, the faintest known black holes up to now.
