Navy communications between mariners, boats and ships can be significantly demanding in terms of quality. Moreover, due to their intermittent connectivity in dynamic scenarios, they require the support of store and forward mechanisms to opportunistically use the available communications and transmit the information related to their operations. However, besides the fact that the communication can be intermittent, it needs to assure a minimum quality whenever communication is possible. This paper proposes an approach for delay tolerant routing based on the quality of the wireless links in navy communications. It measures the quality of the available connections and it uses this information to develop a quality function and a quality-based transitive rule. We propose a delay-tolerant quality-based routing protocol - Quality PRoPHET (Q-PRoPHET), that uses the quality function and transitive rule to determine the best routing decisions. This approach is tested in real indoor and outdoor scenarios that emulate the navy ones. Q-PRoPHET results in better performance than the original PRoPHET in terms of delivery rates, end-to-end delay and packets transmission, which are critical parameters for the communication in navy operations.