The connectivity reliability of strait and canal nodes in seaborne crude oil networks is uncertain because of various risk factors. Existing studies have mainly focused on road networks and often ignored real-world factors by assuming fixed and identical values for the connectivity reliability of each node, leading to inaccurate estimations. Few studies have considered node reliability when identifying the most reliable routes for oil shipments in response to various external and changing risks. To address these limitations, we first establish new connectivity reliability evaluation methods for both nodes and networks. Then, we develop the α-most reliable shipping route and the very most reliable shipping route models using uncertain programming to dynamically identify the most reliable routes for crude oil, ensuring timely and safe transportation. We apply these models to China's seaborne network of imported crude oil. The results show a network connectivity reliability of 0.6228, which is impacted by unreliable origin–destination pairs in the Middle East. The risk values of the most reliable oil shipping routes vary regionally, with higher values in Africa and the Middle East than in Asia and Latin America. As node risk increases, regional disparities also increase. These findings will aid in the development of energy transportation and import strategies to enhance transportation reliability.