Ship arrival in port is a complicated process that involves many parties and requires careful coordination. This paper adds to earlier knowledge on ship arrival processes through a detailed process mining analysis of the ship arrival process in the Port of Antwerp. We employ event logs from AIS data to analyze the coordination process that ports carry out before ships are declared ‘ready to enter’ the port. In addition to our process analysis, we present an analysis of the timing of estimated times of arrival (ETA) communications during the arrival process. We observe that ETAs improve during specific stages of the arrival process. We introduce a new variable – the ‘collapse rate’ which measures the reduction in prediction error and the effectiveness of coordination through the arrival process. Our analysis also reveals challenges when working with AIS data, such as the considerable manual data input and relatively large amounts of extreme outliers. Therefore, all operational systems and traffic management applications in shipping and ports are confronted with unavoidable uncertainties. Finally, our analysis shows that the beginning of the arrival process in port is relatively uncertain, and this raises significant doubts about the practical feasibility of the UNDP/IMO Just-in-Time Shipping program that has recently been launched.