In this paper, we consider the concept of statenorm estimators for switched nonlinear systems under average dwell-time switching signals. State-norm estimators are closely related to the concept of input/output-to-state stability (IOSS). We show that if the average dwell-time is large enough, a non-switched state-norm estimator for a switched system exists in the case where each of its constituent subsystems is IOSS. Furthermore, we show that a switched state-norm estimator, consisting of two subsystems, exists for a switched system in the case where only some of its constituent subsystems are IOSS and others are not, provided that the average dwell-time is large enough and the activation time of the non-IOSS subsystems is not too large. In both cases, the stated sufficient conditions are also sufficient for the switched system to be IOSS. For the case where some subsystems are not IOSS, we also show that the switched state-norm estimator can be constructed in such a way that its switching times are independent of the switching times of the switched system it is designed for.