On 11 March 2020, a lockdown to limit the spread of COVID-19 was implemented in Denmark. The pandemic and the lockdown might have caused stress, depression, and anxiety in new mothers. Individuals with high resilience to stress may have been less affected. This study aimed to investigate if changes in perceived stress, anxiety, depression, and resilience from the second trimester until two months postpartum were different before and during the COVID-19 pandemic in Denmark in spring 2020. Pregnant women enrolled in an ongoing feasibility study completed an online questionnaire measuring perceived stress, depression, anxiety, and resilience in the second trimester and two months postpartum. Changes in scores between women completing the two-month postpartum questionnaire before (n = 26) or during (n = 47) the COVID-19 pandemic were calculated. No statistically significant differences in changes from baseline to follow-up between pre-and during-pandemic groups in Cohen’s Perceived Stress Scale (PSS), the Depression, Anxiety, Stress Scale (DASS), or the Connor–Davidson Resilience Scale (CD-RISC) were found. Adjusted differences in group means were as follows: PSS: 0.70 (CI—2.45; 3.85); DASS Stress: 0.76 (CI—3.59; 2.08); DASS Anxiety: 0.47 (CI—0.84; 1.77); DASS Depression: 0.88 (CI—0.95; 2.71); and CD-RISC: 1.19 (CI—3.16; 5.54). In conclusion, we did not find significant differences in the development of stress, depression, anxiety, or resilience before or during the Danish COVID-19 pandemic in spring 2020.