Battery systems are increasingly being used for powering ocean going ships, and the number of fully electric or hybrid ships relying on battery power for propulsion and maneuvering is growing. In order to ensure the safety of such electric ships, it is of paramount importance to monitor the available energy that can be stored in the batteries, and classification societies typically require that the state of health (SOH) of the batteries can be verified by independent tests – annual capacity tests. However, this paper discusses physics-informed data-driven approaches to online diagnostics for state of health monitoring of maritime battery systems based on a combination of physical knowledge, physic-based models, insights from extensive characterization tests and operational sensor data collected from the batteries during actual operation. This represents an alternative approach to the annual capacity tests for electric ships that is found to be sufficiently robust and accurate under certain conditions. Previous attempts with purely data-driven models, including both cumulative and snapshot models, semi-supervised learning and simple models based on the state of charge did not achieve the required reliability and accuracy for them to be utilized in a ship classification perspective, as presented at previous PHM conferences. However, preliminary results from the physics-informed data-driven method presented in this paper indicate that it can be relied on for independent verification of state of health as an alternative to physical tests. It has been tested on battery cells cycled in laboratory degradation tests as well as on field returns from batteries onboard ships in service. Notwithstanding, further validation and verification of the method is recommended to further build confidence in the model predictions.