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Light yield, time response, afterglow, and thermoluminescence of Ce-doped garnet scintillators and persistent luminescent materials are controlled by a complex interplay between recombination and trapping/detrapping processes. Extensive research has contributed to a good qualitative understanding of how traps, impurities, and the presence of Ce4+ affect the materials properties. In this work we present a quantitative model that can explain the thermoluminescence and afterglow behavior of complex garnets. In particular, the model allows the determination of capture rates and effective capture radii for electrons by traps and recombination centers in Lu1Gd2Ga3Al2O12:Ce garnet ceramics. The model relies on solving a set of coupled rate equations describing charge carrier trapping and recombination in garnet ceramics doped with Ce and also codoped with a known concentration of an intentionally added electron trap, Yb3+. The model is supported by analysis of a complete set of experimental data on afterglow, rise-time kinetics, and X-ray excited luminescence which show that thermoluminescence/afterglow are governed by trapping/detrapping processes following interactive kinetics with dominant recombination channel. The underlying reason for dominant recombination is the presence of a small fraction of Ce4+ (≈2 ppm in the 0.2% Ce-doped sample) which have a very high capture cross section (≈2.7 Å effective radius) because of the Coulomb attractive nature of this recombination center. The quantitative insights on capture cross sections and concentrations of Ce4+ help to better understand the optical properties of Ce-doped garnet scintillators and persistent luminescent materials and serve in optimizing synthesis procedures by tuning the Ce3+/Ce4+ ratio by codoping with divalent cations and annealing in an oxygen-containing atmosphere.