Understanding fish migratory patterns and movements often relies on tags that are externally or internally implanted. Energy harvesting from fish swimming may benefit the state of the art of fish-tags, by increasing their battery lifetime and expanding their sensory capabilities. Here, we investigate the feasibility of underwater energy harvesting from the vibrations of a biomimetic fish tail though piezoelectric materials. We propose and experimentally validate a modeling framework to predict the underwater vibration of the tail and the associated piezoelectric response. The tail is modeled as a geometrically tapered beam with heterogeneous physical properties, undergoing large amplitude vibration in a viscous fluid. Fluid-structure interactions are described through a hydrodynamic function, which accounts for added mass and nonlinear hydrodynamic damping. To demonstrate the practical benefit of energy harvesting, we assess the possibility of powering a wireless communication module using the underwater vibration of the tail hosting the piezoelectrics. The electrical energy generated by the piezoelectrics during the undulations of the tail is stored and used to power the wireless communication device. This preliminary test offers compelling evidence for future technological developments toward self-powered fish-tags.