This work illustrates viscoelastic testing and fractional derivative modelling to describe the thermally induced transformation equivalent viscoelastic damping of NiTiCu SMA ribbons. NiTiCu SMA ribbons have been recently evaluated to manufacture novel honeycombs concepts (conventional and negative Poisson’s ratio) in shape memory alloys for high damping and deployable sandwich antennas constructions. The dynamic mechanical thermal analysis (DMTA) test has been carried out at different frequencies and temperatures, with increasing and decreasing temperature gradients. Thermally induced transformations (austenitic and martensitic) provide damping peaks at low frequency range excitations. On the opposite, the storage moduli are not affected by the harmonic pulsation. As the SMA ribbon increases its stiffness, the damping capacity reduces, and the loss factor drops dramatically at austenite finish temperature. The fractional derivative models provide a compact representation of the asymmetry of the peak locations, as well as the storage modulus change from martensite to austenite phases.