Traditional criteria for comparing alternative Bayesian hierarchical models, such as cross validation sums of squares, are inappropriate for non-standard data structures. More flexible cross validation criteria such as predictive densities facilitate effective evaluations across a broader range of data structures, but do so at the expense of introducing computational challenges. This paper considers Markov Chain Monte Carlo strategies for calculating Bayesian predictive densities for vector measurements subject to differential component-wise censoring. It discusses computational obstacles in Bayesian computations resulting from both the multivariate and incomplete nature of the data, and suggests two Monte Carlo approaches for implementing predictive density calculations. It illustrates the value of the proposed methods in the context of comparing alternative models for joint distributions of contaminant concentration measurements.