This paper presents a dynamic analysis of the free and forced vibration of a free-standing bridge of superelastic shape memory alloy TiNiCuCo film with ultra-low fatigue properties and evaluates its versatility for novel miniature scale damping applications. A thermodynamics-based finite element model is used to simulate the evolution of martensite phase fraction during load-induced martensitic phase transformation. The effects of pre-strain, strain rate and excitation load on the hysteresis of stress-strain characteristics are investigated in order to assess damping energies. The analysis is performed under non-isothermal conditions taking into account heat transfer and rate-dependence of release and absorption of latent heat. We show that damping energy can be maximized by applying an optimum pre-strain. A maximum damping capacity of 0.17 is determined for the case of complete stress-strain hysteresis loop during phase transformation.