Reliable use of Shape Memory Alloys (SMA) in mitigation of extreme load effects requires a deep study of the SMA behavior according to the necessities of the application. Damping the oscillations induced by one storm of three or four days with a strong wind and/or rain usually requires more than one million of working cycles. A SMA damper is checked in to two realistic cables of ELSA and of IFSTTAR. The measurements establish that the SMA damping device reduces drastically the oscillation amplitude. Technical suggestions for the preparation of the dampers built by several SMA wires of NiTi with 2.46 mm of diameter are included. The choice of appropriate length and the choice of the number of required SMA wires are suggested. Moreover, a suitable simulation by proprietary SMA routine inside ANSYS is included.