  We study rare leptonic decays of vector $B$ mesons in the scalar leptoquark
and family non-universal $Z^\prime$ models. We constrain these new couplings by
using the measured branching fractions of $B_{s,d} \to \mu^+ \mu^-$ processes
and the existing $B_{s,d}^0-\bar B_{s,d}^0$ mixing data. We estimate the
branching fractions of $B_{s,d}^* \to \mu^+ \mu^-$ in both the models, which
are found to be reasonably enhanced from their corresponding standard model
values and within the reach of Run 2-3 of LHC.
