  The Galactic globular cluster NGC 3201 is the first Galactic globular cluster
observed to host dynamically-confirmed stellar-mass black holes, containing two
confirmed and one candidate black hole. This result indicates that globular
clusters can retain black holes, which has important implications for globular
cluster evolution. NGC 3201 has been observed as part of the MAVERIC survey of
Galactic globular clusters. We use these data to confirm that there is no radio
or X-ray detection of the three black holes, and present the first radio and
X-ray limits on these sources. These limits indicate that any accretion present
is at an extremely low rate and may be extremely inefficient. In particular,
for the system ACS ID #21859, by assuming the system is tidally locked and any
accretion is through the capture of the companion's winds, we constrain the
radiative efficiency of any accretion to $\leq1.5\times10^{-5}$. We also
combine the radio and X-ray source catalogues from the MAVERIC survey with the
existing MUSE spectroscopic surveys and the HUGS catalogue of NGC 3201 to
provide a catalogue of 42 multiwavelength sources in this cluster. We identify
a new red straggler source with X-ray emission, and investigate the
multiwavelength properties of the sub-subgiant population in the cluster.
