  After the identification of a candidate $\gamma$-ray transient in the error
region of the binary black hole (BBH) merger GW150914 by the \textit{Fermi}
satellite, the question of whether BBH mergers can be associated to
electromagnetic counterparts remains highly debated. Here, we present radio
follow-up observations of GW170608, a BBH merger that occurred during the
second observing run (O2) of the Advanced Laser Interferometer
Gravitational-wave Observatory (LIGO). Our radio follow up focused on a
specific field contained in the GW170608 sky localization area, where a
candidate high-energy transient was detected by the \textit{Fermi} Large Area
Telescope (LAT). We make use of data collected at 1.4\,GHz with the Karl G.
Jansky Very Large Array (VLA), as well as with the VLA Low-band Ionosphere and
Transient Experiment (VLITE). Our analysis is sensitive to potential radio
afterglows with luminosity densities $L_{\rm 1.4\,GHz}\gtrsim
6\times10^{28}$\,erg\,s$^{-1}$\,Hz$^{-1}$. In the most optimistic theoretical
models, $\approx 20\%$ of BBH events occurring in massive hosts could be
associated with outflows as radio luminous as this. Although we find no
evidence for the presence of a radio counterpart associated with the LAT
candidate in the GW170608 error region, our analysis demonstrates the
feasibility of future radio follow-up observations of well localized BBHs.
Comparing our radio upper-limits with theoretical expectations for the radio
afterglows potentially associated with jets launched in BBH mergers, we find
that for jets of energy $\approx 10^{49}$\,erg seen on-axis, only jet angles
$\theta_{jet}\gtrsim 40^{\circ}$ are compatible with the observations.
