While uncertainty is inherent to doing science, it is often excluded from science instruction, especially postsecondary chemistry instruction. There are a variety of barriers to infusing uncertainty into the postsecondary chemistry classroom, including ensuring "productive" struggle with uncertainty, evaluating student engagement with uncertainty, and facilitating engagement in a way that fits within the postsecondary chemistry context. In this study, we aimed to address these difficulties by designing an argumentation task that enables the direct observation of students interacting with epistemic uncertainty. This task was administered as a written assignment to a large-enrollment, second-semester general chemistry course. Student responses were analyzed to generate a rubric that captures the varied ways students grapple with epistemic uncertainty. In accordance with previous literature, we observed students not engaging with the uncertainty (e.g., generating vague, incomprehensible arguments) and selectively engage with the uncertainty (e.g., use data selectively to avoid uncertainty). However, we also observed the qualitatively distinct approaches students utilized to productively manage epistemic uncertainty. Importantly, we believe that these ways of productively handling uncertainty translate to the kinds of scientific reasoning, personal decision making, and socioscientific reasoning that these learners will continue to engage in. Therefore, this work has implications for supporting students' scientific argumentation by offering instructors a practical way to engage their students with uncertainty and a model to interpret and respond to their students.