  Nuclear moments of the antimony isotopes $^{113-133}$Sb are measured by
collinear laser spectroscopy and used to benchmark phenomenological shell-model
and \textit{ab initio} calculations in the valence-space in-medium similarity
renormalization group (VS-IMSRG). The shell-model calculations reproduce the
electromagnetic moments over all Sb isotopes when suitable effective
$g$-factors and charges are employed. Good agreement is achieved by VS-IMSRG
for magnetic moments on the neutron-deficient side for both odd-even and
odd-odd Sb isotopes while its results deviate from experiment on the
neutron-rich side. When the same effective $g$-factors are used, VS-IMSRG
agrees with experiment nearly as well as the shell model. Hence, the wave
functions are very similar in both approaches and missing contributions to the
M1 operator are identified as the cause of the discrepancy of VS-IMSRG with
experiment. Electric quadrupole moments remain more challenging for VS-IMSRG.
