While the use of steel hysteretic dampers has spread in the last decade for both new and retrofitted constructions, the Italian Building Code (IBC), as well as the Eurocode 8, does not provide specific recommendations for the design and verification of structures equipped with this technology. Due to their strong non-linear behavior, the effectiveness of the design with these systems must be verified through non-linear analyses. Non-Linear Time-History analyses (NLTHAs) are the most reliable method, but they are computationally expensive. The aim of the study is to investigate the reliability of non-linear static procedures, allowed by the IBC as an alternative to NLTHAs, for the analysis of buildings equipped with hysteretic devices provided with high damping capability. A parametric study is conducted on two reinforced concrete residential buildings, typical of the Italian residential heritage, retrofitted with hysteretic braces characterized by different stiffness and ductility values. The retrofit design is verified using non-linear analyses, both static and dynamic, considering either natural or artificial accelerograms, as the IBC deems them as equivalent. Within this work, reference is made only to the IBC; however, given the significant similarity between the IBC and the European code, the outcomes are expected to have a broader impact and to be not limited to the Italian context. Therefore, although this work is a preliminary study, it is believed to offer some initial insights on the topic and serve as the foundation for a more in-depth study that could lead to a regulatory revision on the subject.