Background: The COVID-19 pandemic was a global health and economic crisis. In the early phase of the pandemic, studies found that populations were reporting lower levels of mental well-being and high levels of distress and worry. This study investigated potential protective and risk factors such as sociodemographics and psychological factors such as adaptation/coping. Methods: Two convenience samples from Norway and Denmark were recruited during the early phase of the first lockdown in May 2020 using snowball sampling primarily by social media. Measures included the Patient Health Questionnaire-4 (PHQ-4) for screening anxiety and depression, COVID-19 distress, and coping strategies applied during the lockdown. Descriptive analyses were applied as well as bivariate correlations for associations between coping and mental health measures. Results: Levels of anxiety and depression were not alarmingly high, but being young, single, and female constituted a higher risk for poorer mental health. Applying positive reframing strategies was negatively associated with poor mental health and high COVID-19 stress, whereas distraction coping strategies were positively correlated with poor mental health and high COVID-19 stress. Conclusion: Applying positive reframing as a coping strategy may constitute a protective factor for mental health in the early phase of a crisis such as a pandemic. This knowledge may inform public health agencies on how to promote mental health in similar situations in the future. However, longitudinal and qualitative studies are needed to investigate the long-term effects of the different coping strategies applied.