  Regarding trapped-ion microwave-frequency standards, we report on the
determination of hyperfine splittings and Land\'{e} $g_J$ factors of
$^{111,113}$Cd$^+$. The hyperfine splittings of the $5p~^2P_{3/2}$ state of
$^{111,113}$Cd$^+$ ions were measured using laser-induced fluorescence
spectroscopy. The Cd$^+$ ions were confined in a linear Paul trap and
sympathetically cooled by Ca$^+$ ions. Furthermore, the hyperfine splittings
and Land\'{e} $g_J$ factors of the $5s~^2S_{1/2}$ and $5p~^2P_{1/2,3/2}$ levels
of $^{111,113}$Cd$^+$ were calculated with greater accuracy using the
multiconfiguration Dirac--Hartree--Fock scheme. The measured hyperfine
splittings and the Dirac--Hartree--Fock calculation values were cross-checked,
thereby further guaranteeing the reliability of our results. The results
provided in this work can improve the signal-to-noise ratio of the clock
transition and the accuracy of the second-order Zeeman shift correction, and
subsequently the stability and accuracy of the microwave frequency standard
based on trapped Cd$^+$ ions.
