Inelastic deformation of metallic materials is one of the most effective mechanisms for the dissipation of energy input to a structure by an earthquake. Metallic dampers are special devices that resort to this source of energy dissipation, proving to be a cost-efficient solution for the seismic protection of structures. Two important issues arise when implementing metallic dampers in real structures: (1) Inelastic deformations cause damage that must be quantified after an earthquake to decide upon their eventual replacement; (2) dampers must possess an energy dissipation capacity large enough to endure severe earthquakes. This paper focuses on a particular type of metallic damper consisting of slit-plates made of stainless steel, applied to reinforced concrete frames with rocking columns at the first story. In particular, a new damage index based on the metallic magnetic memory (MMM) method is proposed and validated experimentally to quantify the damage of slit plate dampers subjected to cyclic loadings. Further, the seismic response of a frame with rocking columns that incorporate the damper is obtained to demonstrate that it can endure severe earthquakes without failing, and to emphasize the relevance of the proposed MMM damage index that would make its replacement after a severe earthquake unnecessary.