Time-sensitive Wireless Sensor Network (WSN) applications require finite delay bounds in critical situations. This paper provides a methodology for the modeling and the worst-case dimensioning of cluster-tree WSNs. We provide a fine model of the worst-case cluster-tree topology characterized by its depth, the maximum number of child routers and the maximum number of child nodes for each parent router. Using Network Calculus, we derive "plug-and-play" expressions for the endto- end delay bounds, buffering and bandwidth requirements as a function of the WSN cluster-tree characteristics and traffic specifications. The cluster-tree topology has been adopted by many cluster-based solutions for WSNs. We demonstrate how to apply our general results for dimensioning IEEE 802.15.4/Zigbee cluster-tree WSNs. We believe that this paper shows the fundamental performance limits of cluster-tree wireless sensor networks by the provision of a simple and effective methodology for the design of such WSNs.