Abstract The increasing number of mobile Doppler radars used in field campaigns across the central United States has led to an increasing number of high-resolution radar datasets of strong tornadoes. There are more than a few instances in which the radar-measured radial velocities substantially exceed the estimated wind speeds associated with the enhanced Fujita (EF) scale rating assigned to a particular tornado. It is imperative, however, to understand what the radar data represent if one wants to compare radar observations to damage-based EF-scale estimates. A violent tornado observed by the rapid-scan, X-band, polarimetric mobile radar (RaXPol) on 31 May 2013 contained radar-relative radial velocities exceeding 135 m s−1 in rural areas essentially devoid of structures from which damage ratings can be made. This case, along with others, serves as an excellent example of some of the complications that arise when comparing radar-estimated velocities with the criteria established in the EF scale. In addition, it is shown that data from polarimetric radars should reduce the variance of radar-relative radial velocity estimates within the debris field compared to data from single-polarization radars. Polarimetric radars can also be used to retrieve differential velocity, large magnitudes of which are spatially associated with large spectrum widths inside the polarimetric tornado debris signature in several datasets of intense tornadoes sampled by RaXPol.