A tuned viscous mass damper (TVMD) is a tuned mass damper (TMD)–like system that uses an inerter as its mass element. Because a TVMD performs best when it is optimally tuned to the primary system, variation of system properties, such as spring element stiffness and viscous element damping coefficient, from the optimal values may compromise performance. In this research study, a real-time hybrid simulation (RTHS) environment was built to examine the robustness of a TVMD system incorporated into a single-degree-of-freedom (SDOF) structure with respect to variations in the supporting spring stiffness and damping coefficient. In the RTHS testing, a full-scale rotary inertial damper having an apparent mass of 2500 metric tons connected in series with a spring element made of rubber was used as the physical substructure, whereas the primary SDOF structure was modeled as a numerical substructure. Furthermore, a numerical spring element was incorporated in series between the numerical primary structure and the physical rubber element to represent the variation in supporting spring stiffness. Because the silicone oil used in the rotary inerter-damper as a damping material was non–Newtonian fluid, the damping coefficient decreased as damper velocity increased. Thus, the system robustness with respect to damping coefficient can also be examined by varying damper velocity from the design velocity at which the TVMD is optimally designed. Experimental results show that the TVMD system remains effective and, thus, is robust when the system is detuned when the supporting spring stiffness is higher and the damping coefficient is lower than the optimal values facilitating the motion in the damping part, thereby ensuring effective energy dissipation.