A deeper understanding of the effectiveness of adopting devices mounting shape memory alloy (SMA) elements in applications targeted to the mitigation of vibrations is pursued via an experimental approach. During a seismic event, less than 1000 loading-unloading cycles of the alloy are required to mitigate the earthquake effects. However, the aging effects during the time of inactivity prior to the oscillations (several decades characterized by the yearly summer-winter temperature wave) should be considered in order to avoid and/or minimize them. In this paper, the results obtained by carrying out, in different laboratories, fatigue tests on SMA specimens are compared and discussed. Furthermore, the effects of seismic events on a steel structure, with and without SMA dampers, are numerically simulated using ANSYS. Under an earthquake excitation, the SMA devices halve the oscillation amplitudes and show re-centering properties. To confirm this result, an experimental campaign is conducted by actually installing the proposed devices on a physical model of the structure and by evaluating their performance under different excitations induced by an actuator.