A detailed knowledge of the resistivity of high-temperature superconductors in the overcritical current regime is important to achieve reliable numerical simulations of applications such as superconducting fault current limiters. We have previously shown that the combination of fast pulsed current measurements and finite element analysis allows accounting for heating effects occurring during the current pulses. We demonstrated that it is possible to retrieve the correct current and temperature dependence of the resistivity data points of the superconductor material. In this contribution, we apply this method to characterize the resistivity vs. current and temperature of commercial REBCO tapes in the overcritical current regime, between 77 K and 90 K and in self-field conditions. The self-consistency of the overcritical resistivity model rho_OC is verified by comparing DC fault measurements with the results of numerical simulations using this model as input. We then analyze by numerical simulation to what extent using therho_OC model instead of the widely used power-law model rho_PWL affects the thermal and electrical performance of the tapes in the practical case of a superconducting fault current limiter. A remarkable difference is observed between the measured overcritical current resistivity model rho_OC and the power-law resistivity model rho_PWL. In particular, the simulations using the power-law model show that the device quenches faster than with the overcritical resistivity model. This information can be used to optimize the architecture of the stabilizer in superconducting fault current limiters.