  We investigate the decays of the excited $(b\bar q)$ mesons as probes of the
short-distance structure of the weak $\Delta B=1$ transitions. These states are
unstable under the electromagnetic or strong interactions although their widths
are typically suppressed by phase space. As compared to the pseudoscalar $B$
meson, the purely leptonic decays of the vector $B^*$ are not chirally
suppressed and are sensitive to different combinations of the underlying weak
effective operators. An interesting example is $B^*_s\to \ell^+\ell^-$, which
has a rate that can be accurately predicted in the standard model. The
branching fraction is $\mathcal{B}\sim10^{-11}$, irrespective of the lepton
flavor and where the main uncertainty stems from the unmeasured and
theoretically not-well known $B_s^*$ width. We discuss the prospects for
producing this decay mode at the LHC and explore the possibility of measuring
the $B_s^*\to\ell\ell$ amplitude, instead, through scattering experiments at
the $B_s^*$ resonance peak. Finally we also discuss the charged-current
$B_{u,c}^*\to\ell\nu$ decay which can provide complementary information on the
$b\to u\ell\nu$ and $b\to c\ell\nu$ transitions.
