Ports, often located on the outskirts of (smart) cities, are striving for innovative technological solutions to attain efficiency gains to cope with raising trade volumes and energy savings towards improving their environmental footprint. With two-thirds of the world's major ports located in urban areas, these efforts do not take place in isolation, but in intersection with the multi-layered processes of the smart city. In this context, digital twinning can be a technology with the potential to significantly increase the efficiency of the multi-layered and interconnected ports and smart cities processes. While digital twins for the complex systems of the smart cities have gained momentum in recent years, digital twinning of ports is often narrowed to address only specific port assets. The aim of this article is to investigate how smart city digital twins tackle complex processes and how ports can draw from this experience. We discuss potential interfaces between a port digital twin and a city digital twin. It becomes evident that both these domains of application of digital twinning are complex systems having overlaps and functional interconnections. The paper presents how the port's digital twin can contribute to threat detection, energy savings, cost reductions, performance gains, and improved stakeholder cooperation, based on insights from the city digital twin. Finally, the three overlap points maintenance of shared infrastructure, intelligent joint approaches to avoid congestion, and energy are identified as intersection points.