Due to the COVID-19 pandemic, emergency healthcare workers have come under even more pressure than before, threatening the workers’ mental health and the continuity of care delivered by their teams. This study aims to investigate what conditions increase individual and team resilience, referring to the ability to “bounce back” from stressful situations. We also assess whether team resilience is the sum of the individual resilience of team members, or whether other conditions enhance team resilience and thus continuity of care, despite limited individual resilience. We collected survey data from 129 emergency healthcare team members in the Netherlands to examine to what extent transformational leadership and team familiarity influence the level of team resilience, either directly or mediated by individual resilience, accounting for psychological characteristics and social support. The results show two distinct pathways to enhance team resilience, directly by familiarizing team members with each other and by mobilizing family support, and indirectly but with a much weaker effect, by encouraging team members’ individual resilience through transformational leadership and staffing optimistic team members with high levels of self-efficacy.