One of the most important challenges of modern shipping is the problem of improving the level of safety at sea and enhancing accident-free ship operation. World fleet accident rates have a direct impact on both the safety of human life at sea and on the environment. Ship collisions have a particular place in accident statistics. They are caused by increasing ship deadweight, growing speeds, dense traffic and the presence of navigational hazards, which, combined, considerably increase navigation complexity, especially in coastal and restricted waters. These factors contribute to emergencies, incidents and situations, which, in turn, are characterized by rapidly changing circumstances. The aforementioned features of the navigation process call for the development and application of modern methods of operation and flexible evaluation of the situation at hand, as well as for the development of new approaches to evasive maneuver selection, including computer and information technologies, to ensure the safety of navigation. Thus, the development of modern methods and ways of prompt selection of an appropriate evasive maneuver to alter a ship's course or speed, which is the subject of this paper, is an important research trend. The paper also proposes a method of prompt evasive maneuver selection to prevent collisions by altering the ship's course or reducing its speed by active and passive braking. Analytical expressions used to calculate the limits of unacceptable ship course and ship speed values, taking into account the braking mode, are presented. The author's recommended optimum evasive maneuver is presented, and a technique of prompt evasive maneuver selection aimed at altering a ship’s course or speed by active and passive braking is developed.