Smart mobility is transforming the way the current transportation network is envisioned. It holds the promise of a more sustainable, safer, and efficient future for commuters. Nevertheless, traffic management centers are constantly facing the challenges of ensuring that transportation system components are operating as expected and in a safe manner. As a result, research efforts on improving traffic monitoring aim to design and implement novel approaches for safety applications. In this paper, we adopt formal methods to specify and apply reason to the traffic network’s complex properties. Formal methods provide a framework to rigorously define the safe operation of the traffic network by capturing non-conforming travel behavior, exploring various possible states of vehicular traffic, and detecting any irregularities that may arise. In this work, a new approach to traffic monitoring is proposed, which uses specification-based monitoring. We develop monitors that define traffic parameters, such as conforming to speed limits and maintaining appropriate headway. A formal language known as Signal Temporal Logic is used to specify and analyze these traffic rules. The proposed framework is then applied to a calibrated micro-simulated highway network to identify whether individual vehicle trajectories violate or satisfy the proposed specifications. Statistical analysis of the outputs shows that our proposed approach is effective in differentiating between violating and conforming vehicles. This approach can be used by traffic management centers that are seeking to accommodate emerging mobility technologies that are autonomous and connected. In particular, the presented work can be valuable in studying traffic stream properties, identifying possible hazards, and providing valuable feedback for automating traffic monitoring systems.