  In this work, we first perform a systematic study of the transition magnetic
moments and the corresponding radiative decay behaviors of the $B_c$-like
molecular states associated with their mass spectra, where the constituent
quark model is adopted by considering the $S$-$D$ wave mixing effect. Our
numerical results show that the radiative decay properties can be considered as
the effective physical observable to reflect the inner structures of these
$B_c$-like molecular states. Meanwhile, we also discuss the magnetic moments of
the $B_c$-like molecular states, and we find that the magnetic moment
properties can be used to distinguish the $B_c$-like molecular states from the
conventional $B_c$ mesonic states, which have the same quantum numbers and
similar masses. We expect that the present study can inspire the interest of
the experimentalist in exploring the electromagnetic properties of the
$B_c$-like molecular states, especially the radiative decay properties.
