The concept of autonomous merchant ships is quite recent. The increasing interest in autonomous vessels is nowadays calling for smart technologies that are supposed to replace the human actions on board. This involves troublesome issues related to ship safety. In the future, decision-making processes that are conventionally performed by human beings on board ship will be moved ashore to the control centre and maybe even completely replaced by computers and smart technologies. This paper proposes a method suitable for oceangoing ships, providing an autonomous routine for the avoidance of two dangerous phenomena involving excessive motions of the ship, e.g. the synchronous roll and the parametric resonance, both taking place in rough seas. The method is two-fold, since it pertains to the process of route planning and route monitoring and it encompasses two submethods (A and B). Submethod A is used to define a set of operational scenarios to be avoided due to excessive accelerations, with the use of a numerical ship motion model. This is applied at the route-planning stage. Submethod B is developed to monitor ship motions and to detect large roll motion for a ship in the seaway. It also raises alerts at two levels, first when the large roll motions are expected to develop (leaving ample time for remotely located operators to react), second when the large roll motions are developing (leaving a short time window for action taken on board the ship). The main sources of uncertainty are defined and the solutions to address those are proposed. Finally, the method is applied on simulated time histories of ship motion, which is a container ship traversing the Pacific Ocean. The obtained results are promising; however, further work is required with respect to various manoeuvers performed by a ship in the seaway.