In this paper, we discuss situations in which disagreement or conflict arises in the critical care setting in relation to the determination of death by neurologic criteria, including the removal of ventilation and other somatic support. Given the significance of declaring a person dead for all involved, an overarching goal is to resolve disagreement or conflict in ways that are respectful and, if possible, relationship preserving. We describe four different categories of reasons for these disagreements or conflicts: 1) grief, unexpected events, and needing time to process these events; 2) misunderstanding; 3) loss of trust; and 4) religious, spiritual, or philosophical differences. Relevant aspects of the critical care setting are also identified and discussed. We propose several strategies for navigating these situations, appreciating that these may be tailored for a given care context and that multiple strategies may be helpfully used. We recommend that health institutions develop policies that outline the process and steps involved in addressing situations where there is ongoing or escalating conflict. These policies should include input from a broad range of stakeholders, including patients and families, as part of their development and review.