Negative effects on the port environment can originate from ports’ hinterland, ports’ activities and operations, and from ships. According to the available literature and long-lasting experience of numerous ports presented in different sources, pollution from ships belongs to the group of environmental priorities in ports. After a theoretical introduction where the importance of ports, their development, and the challenges/risks faced by ports (with special attention to environmental risks) are analyzed, an overview of the literature from the domain of prevention of pollution from ships is presented. Based on the standard structure of the PDCA (Plan, Do, Check, Act) management cycle, in this paper, a process model of the management (sub)system of prevention of pollution from ships in a port is proposed. Key demands related to the modeled (sub)system and bases which directly determine those demands are made concrete through an analysis of a case study: the Port of Bar (Montenegro). A categorization of domains of risks of pollution from ships in the analyzed port is conducted using the Analytic Hierarchy Process (AHP) method: considerations are based on a three-level hierarchy model: “0”—goal; level “1”—criterion; and level “2”—choice. The results of the analyses show that a domain with the highest rank of risk of pollution from ships is variant (alternative) M1: unloading oil/oil derivatives from ships to tanks (and vice versa), with a composite weight of 0.5365 (53.65%). The results of considerations presented in this paper can be used in a process of optimization of the (sub)system of prevention of pollution from ships in a multipurpose port as well as a reliable base for further research in this domain.