Coronavirus disease (COVID-19) causes various vascular and blood-related reactions, including exacerbated responses. The role of endothelial cells in this acute response is remarkable and may remain important beyond the acute phase. As we move into a post-COVID-19 era (where most people have been or will be infected by the SARS-CoV-2 virus), it is crucial to define the vascular consequences of COVID-19, including the long-term effects on the cardiovascular system. Research is needed to determine whether chronic endothelial dysfunction following COVID-19 could lead to an increased risk of cardiovascular and thrombotic events. Endothelial dysfunction could also serve as a diagnostic and therapeutic target for post-COVID-19. This review covers these topics and examines the potential of emerging vessel-on-a-chip technology to address these needs. Vessel-on-a-chip would allow for the study of COVID-19 pathophysiology in endothelial cells, including the analysis of SARS-CoV-2 interactions with endothelial function, leukocyte recruitment, and platelet activation. “Personalization” could be implemented in the models through induced pluripotent stem cells, patient-specific characteristics, or genetic modified cells. Adaptation for massive testing under standardized protocols is now possible, so the chips could be incorporated for the personalized follow-up of the disease or its sequalae (long COVID) and for the research of new drugs against COVID-19.