  We present results of a lattice QCD calculation of $B\to D^*$ and $B_s\to
D_s^*$ axial vector matrix elements with both states at rest. These zero recoil
matrix elements provide the normalization necessary to infer a value for the
CKM matrix element $|V_{cb}|$ from experimental measurements of $\bar{B}^0\to
D^{*+}\ell^-\bar{\nu}$ and $\bar{B}^0_s\to D_s^{*+}\ell^-\bar{\nu}$ decay.
Results are derived from correlation functions computed with highly improved
staggered quarks (HISQ) for light, strange, and charm quark propagators, and
nonrelativistic QCD for the bottom quark propagator. The calculation of
correlation functions employs MILC Collaboration ensembles over a range of
three lattice spacings. These gauge field configurations include sea quark
effects of charm, strange, and equal-mass up and down quarks. We use ensembles
with physically light up and down quarks, as well as heavier values. Our main
results are $\mathcal{F}^{B\to D^*}(1)= 0.895\pm
0.010_{\mathrm{stat}}\pm{{0.024}_{\mathrm{sys}}}$ and $\mathcal{F}^{B_s\to
D_s^*}(1)= 0.883\pm 0.010_{\mathrm{stat}}\pm{0.028_{\mathrm{sys}}}$. We discuss
the consequences for $|V_{cb}|$ in light of recent investigations into the
extrapolation of experimental data to zero recoil.
