This paper addresses the problem of repositioning empty containers in maritime networks under possible port disruptions. Since drastically different futures may occur, the decision making process for dealing with this problem cannot ignore the uncertain nature of its parameters. In this paper, we consider the uncertainty of relevant problem data by a stochastic programming approach, in which different scenarios are included in a multi-scenario optimization model and linked by non-anticipativity conditions. Numerical experiments show that the multi-scenario solutions provide a hedge against uncertainty when compared to deterministic decisions and exhibit some forms of robustness, which mitigate the risks of not meeting empty container demand.