T he problem of estimating delays experienced by customers with different priorities, and the determination of the appropriate delay announcement to these customers, in a multi-class call center with time varying parameters, abandon-ments, and retrials is considered. The system is approximately modeled as an M(t)/M/s(t) queue with priorities, thus ignoring some of the real features like abandonments and retrials. Two delay estimators are proposed and tested in a series of simulation experiments. Making use of actual state-dependent waiting time data from this call center, the delay announcements from the estimated delay distributions that minimize a newsvendor-like cost function are considered. The performance of these announcements is also compared to announcing the mean delay. We find that an Erlang distribution-based estimator performs well for a range of different under-announcement penalty to over-announcement penalty ratios.