The COVID-19 pandemic has brought unique challenges for caregivers. This study examines whether individual resilience accounted for differences in caregiver burden, coping-related resilient behaviors, depression, and stress during the COVID-19 lockdowns. A total of 324 caregivers responded to a survey covering three time points (pre-pandemic (t0, retrospective), first lockdown in April 2020 (t1, retrospective), and second lockdown in winter 2020/2021 (t2, prospective)). Items covered the care situation and caregiver burden (t0 and t1), coping-related resilient behavior (t1), perceived stress (PSS-10) and depression (GDS-15) (t1 and t2) as well as resilience (BRS) (t2). Higher resilience was associated with lower caregiver burden, a higher degree of coping-related resilient behaviors, and with lower perceived stress but higher depression. Stress and depression showed different trajectories over time depending on resilience. Resilience-promoting interventions for caregivers should be used to reduce stress and caregiver burden. Special attention should be paid to depression prevention, with tailored programs to address the needs of resilient caregivers during lockdowns.