The electromagnetic (EM) wave attenuation by building walls is experimentally investigated, focusing on the frequency range 700 MHz-5 GHz. The results of this research can be used in the planning of the indoor radio coverage of wireless access networks like 2G, 3G, 4G, WiFi, and future 5G mobile phone systems, in the study of satellite navigation applications, and in the evaluation of the resident population exposure to electromagnetic fields emitted by the radio base stations (RBSs) of the mobile phone radio access network (RAN). Measurements are obtained using a portable vector network analyzer (VNA) connected to two light Vivaldi antennas. Time-domain methods are used to reduce errors caused by multiple paths. Measurements of EM building wall attenuation have been carried out in the city of Rome, Italy, in different buildings topologies: historical buildings from the Roman Empire up to middle 19th-century and modern reinforced concrete buildings. Measurements of EM shielding effectiveness (SE) show values even greater than 80 dB.