In this research we develop an estimation methodology for a system of simultaneous equations where the endogenous variables are subject to censorship and where the data follows a panel structure. The likelihood function of such a model presents several complications, so that traditional optimization procedures cannot be employed. We propose the application of a simulation-based estimator that mimics the Expectation-Maximization (EM) algorithm and also inherits its likelihood-maximizing properties. Simulation exercises for both random-effects and fixed-effect models verify that this estimation methodology performs remarkably well in comparison to traditional methods, without a high cost in terms of loss of efficiency. The same idea is then extended to other types of data limitations and to a dynamic model.