Trust-aware routing in wireless sensor networks (WSNs) is a crucial problem that has drawn the attention of researchers. The motivation for tackling this problem arises directly from the highly constrained nature of a WSN and its easy exposure to insecure conditions. In this regard, reputation-based solutions are used to provide trust-aware routing. However, this approach requires that a node needs to continuously monitor its environment to detect misbehaviour events. This is considered to be a costly operation for WSN nodes because of its resource scarcity. Here, the authors propose a reputation system-based solution for trust-aware routing, which implements a new monitoring strategy called an efficient monitoring procedure in a reputation system (EMPIRE). EMPIRE is a probabilistic and distributed monitoring methodology that tries to reduce the monitoring activities per node while maintaining the ability to detect attacks at a satisfactory level. The proposed procedure has been evaluated using the Monte Carlo simulation. New evaluation methodologies are introduced to test and explore the efficiency of our proposed procedure. Simulation results of the reputation system show that reducing monitoring activities with EMPIRE does not have a significant impact on system performance in terms of security.