This paper investigates the performance of cache-aided systems with heterogeneous caches and secure delivery. In particular, we consider users with unequal caches and assume the signals transmitted during the delivery phase to be overheard by an external eavesdropper which must not gain any information about the system's files. We study server-based delivery and device-to-device-based delivery where the server does not participate in the delivery phase. For each scenario, assuming uncoded placement and linear delivery schemes, we provide an optimization framework to minimize the secure delivery load. We show that the secure delivery requirement can be satisfied by modifying the memory capacity constraints in the non-secure framework to take into account the cost of caching keys. In addition, we show that the cost of secure delivery is negligible for caching systems with large number of files.