COVID-19 pandemic has had a major impact on most aspects of everyday life and that has led to a significant faster evolution in the digitalization of medical services. Telemedicine and eHealth continue to provide solutions to mitigate this pandemic’s effects, with the aim of helping isolated coronavirus patients, as well as people with chronic conditions. This paper presents how COVID-19 pandemic has been influencing the development of remote healthcare monitoring systems as a result of the need to maintain a remote communication between patient and medical specialist and to provide reliable care. In order to demonstrate how a remote healthcare monitoring scenario can be optimized and personalized according to the needs, specificities and the evolving health status of a patient, the building of the Healthcare Monitoring Component from the ongoing RO-SmartAgeing system is presented. This component, based on a series of medical sensors, connected to an Arduino board that collects and transmits data, through a Wi-Fi network, to the Fog/ Edge level, offers both the means to real-time monitor the patient’s vital signs and to alert healthcare specialists in case of an abnormal measured value. The gathered information is filtered and then sent to a database in the Cloud allowing further analysis and health data-based applications to be provided. The benefits of this solution that allows the real time visualization of medical data, as well as its storage, processing and subsequent analysis are highlighted and correlated with the specificities induced by COVID-19 pandemic.