The optical transitions in ${\mathrm{Ce}}^{3+}$:${\mathrm{Y}}_{3}$${\mathrm{Al}}_{5}$${\mathrm{O}}_{12}$ from the lowest 5d excited state of the ${\mathrm{Ce}}^{3+}$ ion to the host conduction band have been investigated. Two spatially overlapped and time-sequenced laser pulses were used to observe directly the excited-state absorption (ESA) and the two-step photoionization of the cerium ions. The peak cross section of the ESA transition is (1.0\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}17}$ ${\mathrm{cm}}^{2}$ at 700 nm. The ESA spectrum was measured from 600 to 880 nm and is used to construct an energy-level diagram for the ${\mathrm{Ce}}^{3+}$ ions relative to the energy-band states of the ${\mathrm{Y}}_{3}$${\mathrm{Al}}_{5}$${\mathrm{O}}_{12}$ host. The energy gap between the lowest relaxed 5d state and the conduction-band edge is estimated to be 10 000 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$. Strong-probe saturation measurements indicate a slow and inefficient back-transfer of excitation to the cerium ions following the ESA. Photoconductivity measurements were used to confirm the two-step photoionization of the cerium ions.