  High-pressure structural searches of superhydrides CeBeH$_8$ and CeBH$_8$
were performed under ambient pressure up to 300 GPa. We identify
$Fm\overline{3}m$-CeBeH$_8$ with a superconducting transition temperature
$T_{c}$ of 56 K at 10 GPa. Two more phases with spacegroup $R\overline{3}m$ and
$C2/m$, were investigated within the increasing pressures. CeBH$_8$ shows a
similar phase transition process as CeBeH$_8$ but with higher transition
pressures and higher $T_c$. $Fm\overline{3}m$-CeBH$_8$ is predicted to be
superconducting above 120 GPa with a maximum $T_{c}$ of 118 K at 150 GPa.
$R\overline{3}m$-CeBH$_8$ and $C2/m$-CeBH$_8$ are dynamically stable above 120
GPa and 100 GPa, respectively. The maximum $T_{c}$ is 123 K at 195 GPa for
$R\overline{3}m$-CeBH$_8$, and 115 K at 350 GPa for $C2/m$-CeBH$_8$. Our work
enriches the family of ternary hydrides and may provide a useful guideline for
further search for superconducting hydrides at low and moderate pressures.
