Radar satellites allow the collection of data on large areas without direct access to structures. Thereby, they appear very attractive for Structural Health Monitoring (SHM) purposes. Data collected by satellites can be processed to obtain temporal histories of displacements through which the health state of a monitored system can be potentially identified. However, anomalies in the time histories of displacements are not necessarily due to damage. Environmental phenomena, such as variations in atmospheric temperature, and rain, can modify the behavior of structures without compromising their safety. The impact of these phenomena on the structural response can hinder the identification of anomalies or lead to false alarms if such alterations are misinterpreted as damage. Furthermore, if the monitored system is a historical structure, uncertainties on the structural behavior are inevitably increased during aging. The purpose of this article is to discuss the possibility of identifying damage due to seismic actions considering the impact of variations of environmental factors on the time histories of the displacements retrieved by satellite data. The structural health condition of a historical structure located in the city of Rome (Italy) hit by the October 2016 Central Italy earthquakes is investigated based on interferometric satellite data. The satellite data are acquired by COSMO-SkyMed (CSM) of the Italian Space Agency between 2010 and 2019 and are processed by CNR IREA.