Damages in port facilities during past seismic events have led to widespread direct and indirect losses, with serious impact on the economic, operational, and emergency management of the port itself and, as a consequence, on the related society. Ground shaking is among the most widespread sources of seismic damage to port structures and infrastructure, together with the induced phenomena principally associated with the liquefaction of loose, saturated soils that often prevail in coastal areas. This study presents a methodology for the seismic risk assessment of port facilities which considers the combined effects of ground shaking and liquefaction as well as various interdependencies among port elements, which affect the port’s operation and, consequently, the total risk impact. The methodology, based on either probabilistic or deterministic scenario-based approaches, is demonstrated through an application to the Thessaloniki port, one of the most important ports in Southeastern Europe and the largest transit-trade port in Greece. The systemic risk analysis of the port is carried out using as a performance indicator the reduction in the container and bulk cargo movements affected by the seismic performance of the piers, the waterfront, and container/cargo handling equipment, as well as their interaction with the seismic performance of the electric power system. Two different functionality analyses of the port system are performed, one basic and one less conservative alternative. The results of the probabilistic seismic risk assessment are illustrated in terms of annual probabilities of collapse and loss exceedance curves for each individual port component as well as normalized performance loss for the whole port system for the container and cargo terminal. For the scenario-based deterministic approach, the results are given in terms of risk maps presenting the spatial distribution of damages/losses for all components as well as in terms of the expected loss of performance of the port system. The proposed methodology may provide the basis for an efficient seismic risk management of ports. It may also be adjusted and applied to other port infrastructures in Greece and worldwide considering additional components, interactions among elements, and different earthquake induced hazards.