Nonlinear Energy Sinks (NES) are passive vibration absorbers composed of a small inertia and a smooth nonlinear stiffness with linear viscous damping. The main advantage of a NES is its lack of preferential natural frequency, then NESs can resonate over a wide range of frequencies and with any mode of the primary structure to which they are connected. These kind of absorbers however, are energy-dependent devices limited by energy thresholds where optimal design regions can be very close to low effective ones. It is then frequent that changes in the exciting energy levels can significantly reduce the performance of previously tuned NESs. The NES energy sensibility, limit its capabilities to control vibrations in structures subject to seismic induced excitations. Preliminary studies have shown that this sensitivity can be reduced by properly tuning the NES damping but no formal procedure exist. In this work we present a numerical methodology to tune the NES parameters by defining an index that quantifies the effect that NES damping has on the absorber robustness. A three-story shear building model subject to random seismic ground excitation is used to introduce the concepts and the methodology.