In this paper, the potential hinterland of the new container terminal of the port of Leghorn (Livorno in Italian) is studied. The study actually analyses the competitiveness of major European ports with respect to some of the most contestable regions in Europe. Travel time and monetary costs of railway paths, connecting ports to their hinterland, have been determined. The rail network of a large part of Europe was modelled using a graph. To each link, which represents a portion of the rail line, a cost function is associated. The travel time on the link is determined from the average speed, which has been determined from the maximum speed via formulae obtained through linear regression. The few cost functions that exist in current literature for the computation of the cost of a rail link are not detailed enough. Therefore, a new cost function has been developed. All cost components were determined in detail: the staff cost, the amortisation, maintenance, and insurance costs of locomotives and wagons, the cost of the usage of rail track, the traction cost. The traction cost was calculated in detail from all resistances to motion. Moreover, for each rail link, the number of locomotives needed to operate the train and the maximum towable weight were determined. The monetary value of time in freight transport registers a high variability; therefore, three different optimisations of the paths—by travel times, monetary costs, and generalised costs—between each origin–destination pair were carried out. The rates of competitiveness of the ports with respect to the examined European contestable regions were analysed.