Due to scalability issues in this area, Network-on-Chip (NoC) has recently become the standard for modern communication infrastructures in Multiprocessor System-on-Chip. Nevertheless, such systems are vulnerable to the security threats that injected Hardware Trojans (HTs) impose. In this paper, we consider HTs within the NoC routers and focus on detecting those HTs through trust evaluation metrics. We then apply trust-based adaptive routing to increase the reliability of the communication and to circumvent HTs. We compare different trust metrics, which we combined with adaptive routing algorithms, and evaluate their impact using PANACA as NoC simulation platform. Moreover, we provide meaningful measures regarding the reliability of the detection of HTs through trust evaluation metrics and the imposed storage overhead of such approaches. Our results show, that we increase the reliability of the communication by 9% to 12% and route between 40% to 50% less flits through nodes infected by a HT.