This work presents and assesses a reduced model of a recently proposed seismic isolation system, namely the Roll-N-Cage isolator. This system incorporates several interesting features and mechanisms in a single unit, among others: isolation, energy dissipation, buffering, high vertical stiffness and strength for supporting heavy loads. Departing from previous studies, which were based on the simulation of the Roll-N-Cage device by uncoupled orthogonal unidirectional models, this work first introduces a reduced-order coupled bidirectional numerical model of the device. Then the efficiency of such a type of control devices, as simulated by the proposed approach, is evaluated for the seismic protection of a cable-supported bridge. The bridge model is derived from the ASCE benchmark cable-stayed bridge by means of an extended version. It was found that the developed model with optimal tuning of the parameters was proved able to match satisfactorily the physical behavior of the RNC devices, which were found able to achieve effective reductions in the seismic effects in terms of both internal forces and accelerations. It was also noted that choosing small buffer stiffness of the buffer or self-stopping mechanism could slightly limit the peak displacements, at cost of a small increment of the deck accelerations and non-remarkable variations of internal forces. Further, a coupled bidirectional model seems to be fundamental to precisely predict the actual behavior of the isolators when the deck motion is affected by a non-negligible interaction in the two (longitudinal-transversal) directions.