  CeCd$_3$P$_3$ and CeCd$_3$As$_3$ compounds adopt the hexagonal
ScAl$_3$C$_3$-type structure, where magnetic Ce ions on a triangular lattice
order antiferromagnetically below $T_\text{N} \sim$0.42~K. Their crystalline
electric field (CEF) level scheme has been determined by fitting magnetic
susceptibility curves, magnetization isotherms, and Schottky anomalies in
specific heat. The calculated results, incorporating the CEF excitation, Zeeman
splitting, and molecular field, are in good agreement with the experimental
data. The CEF model, with Ce$^{3+}$ ions in a trigonal symmetry, explains the
strong easy-plane magnetic anisotropy that has been observed in this family of
materials. A detailed examination of the CEF parameters suggests that the
fourth order CEF parameter $B_{4}^{3}$ is responsible for the strong CEF
induced magnetocrystalline anisotropy, with a large $ab$-plane moment and a
small $c$-axis moment. The reliability of our CEF analysis is assessed by
comparing the current study with earlier reports of CeCd$_{3}$As$_{3}$. For
both CeCd$_{3}X_{3}$ ($X$ = P and As) compounds, less than 40 \% of $R\ln(2)$
magnetic entropy is recovered by $T_\text{N}$ and full $R\ln(2)$ entropy is
achieved at the Weiss temperature $\theta_{p}$. Although the observed magnetic
entropy is reminiscent of delocalized 4$f$-electron magnetism with significant
Kondo screening, the electrical resistivity of these compounds follows a
typical metallic behavior. Measurements of thermoelectric power further
validate the absence of Kondo contribution in CeCd$_{3}X_{3}$.
