Duration data are often subject to various forms of censoring that require adaptations of the likelihood function to properly capture the data generating process, but existing spatial duration models do not yet account for these potential issues. Here, we develop a method to estimate spatial-lag duration models when the outcome suffers from right censoring, the most common form of censoring. We adapt Wei and Tanner's (1991) imputation algorithm for censored (non-spatial) regression data to models of spatially interdependent durations. The algorithm treats the unobserved duration outcomes as censored data and iterates between multiple imputation of the incomplete, that is, right censored, values and estimation of the spatial duration model using these imputed values. We explore the performance of an estimator for log-normal durations in the face of varying degrees of right censoring via Monte Carlo and provide empirical examples of its estimation by analyzing spatial dependence in states' entry dates into World War I.