The cell-loss ratio at a given node in an ATM switch, defined as the steady-state fraction of packets of information that are lost at that node due to buffer overflow, is typically a very small quantity which is hard to estimate by simulation. Cell losses are rare events and importance sampling is normally the appropriate tool in this situation. However, finding the right change of measure is generally hard. In this paper, importance sampling is applied to estimate the cell-loss ratio in an ATM switch modeled as a queueing network fed by several sources emitting cells according to a Markov-modulated on/off process, and where all the cells from the same source have the same destination. The numerical experiments show impressive efficiency improvements.