We employ right-censored Poisson point process models to develop maximum-likelihood procedures for estimating the time of arrival of transient optical signals subject to saturation distortion. The Poisson intensity is modeled as a template with an unknown scaling factor with additive background counts. Using Monte Carlo simulations, we explore the performance of different algorithms as a function of signal magnitude and saturation threshold. In particular, we characterize the benefit our procedures have over algorithms that are unaware of the censoring.