Bridges connecting islands close to the coast and crossing the sea have been attracting the attention of several researchers working in the field of train–bridge interactions. A runability analysis of a bridge during the event of a ship impact with a pier is one of the most interesting and challenging scenarios to simulate. The objective of the present paper is to study the impact on the running safety of a train crossing a sea bridge as a function of different operational factors, such as the train travelling speed, the type of impacting ship, and the impact force magnitude. Considering train–bridge interactions, a focus is also placed on wheel–rail geometrical contact profiles, considering new and worn wheel–rail profiles. This work is developed considering a representative continuous deck bridge with pier foundations located on the sea bed composed of six spans of 80 m. Time-domain simulations of trains running on the bridge during ship impact events were carried out to quantify the effect of different operating parameters on the train running safety. For this purpose, derailment and unloading coefficients, according to railway standards, were calculated from wheel–rail vertical and lateral contact forces. Maps of the safety coefficients were finally built to assess the combined effect of the impact force magnitude and train speed. The present investigation also showed that new wheel–rail contact geometrical profiles represent the most critical case compared to moderately worn wheel–rail profiles.