In this work, a detailed analysis is presented on the propagation of electromagnetic (EM) fields produced by a radiofrequency identification (RFID) system that operates in the UHF band, considering the response of a set of passive tags immersed in the field, after analyzing the possible antenna configurations relevant to tags. The technical literature is lacking of specific studies about the EM behavior of RFID systems in critical environments, especially where medical equipment is used. Therefore, we decided to evaluate the radiation of an RFID reader through a series of delicate steps, starting from the analysis of rules that govern the RFID devices themselves up to the methodologies for the measurements established by the Italian Committee of Electrotechnics. We also carried out immunity measures of an infusion pump, which is an electrical equipment to support vital functions. Its behavior was evaluated in the presence of the EM field radiated by the RFID reader. Even at this stage, we have followed the existing standards, both for medical devices and for the procedures used for the experimental measures.