Epistemic beliefs and emotions can exert a profound effect on individuals' academic motivation and achievement. This study presents a plausible model to explore the relationships among engineering students' epistemic beliefs, epistemic emotions, and their use of problem-solving strategies within project design contexts. Findings from path analysis indicate that students who believe design-related engineering knowledge should be justified in multiple ways demonstrate a higher level of positive epistemic emotions. Those who believe foundational engineering knowledge is uncertain and evolving show a lower level of boredom when confronted with design problems. Students experiencing positive epistemic emotions tend to use more problem-solving strategies in their design projects, leading to higher achievement in the design course. Those grappling with boredom tend to use fewer problem-solving strategies, resulting in lower achievement in the design course. Connections between epistemic cognition research and instructional practices in engineering education are discussed.