We develop customer delay predictors for multi-skill call centers that take as inputs the queueing state upon arrival and the waiting time of the last customer served. Many predictors have been proposed and studied for the single queue system, but barely any predictor currently exists for the multi-skill case. We introduce two new predictors that use cubic regression splines and artificial neural networks, respectively, and whose parameters are optimized (or learned) from observation data obtained by simulation. In numerical experiments, our proposed predictors are much more accurate than a popular heuristic that uses, as a predictor, the delay of the last customer of the same type that started service.