Recent studies were dedicated to the realization of measurements on stay-cable samples of different geometry and static conditions as available at several facilities. The elaboration of the acquired data showed a a satisfactory efficacy of the dampers made of NiTi wires in smoothing the cable oscillations. A further attempt to investigate the applicability of the achieved results beyond the specific case-studies represented by the tested cable-stayed samples is herein pursued. Comparative studies are carried out by varying the diameter of the NiTi wire so that similar measurements can be taken also from laboratory steel cables of reduced size. Details of the preparation of the Ni-Ti wires are discussed with particular attention being paid to the suppression of the creep phenomenon. The resulting shape of the hysteretic cycle differs according to the wire diameter, which affects the order of the fitting polynomial to be used when trying to retrieve the experimental results by numerical analyses. For a NiTi wire of given diameter, an estimate of the amount of dissipated energy per cycle is given at low levels of maximum strain, which correspond to a fatigue fracture life of the order of millions of cycles. The dissipative capability is affected by both the temperature and the cycling frequency at which the tests are performed. Such effects are quantified and an ageing process is proposed in order to extend the working temperature range of the damper to cold weathers typical of the winter season in Northern Europe and Canada. A procedure for the simulation of the shape memory alloy behavior in lengthy cables by finite element analysis is eventually outlined.