Two power law relations linking equivalent radar reflectivity factor (Ze) and snowfall rate (S) are derived for a Micro Rain Radar (MRR), which operates at K-band, and a W-band cloud radar. For the development of these Ze-S relationships, a dataset of calculated and measured variables is used. Surface-based video-disdrometer measurements were collected during snowfall events over five winters at the high-latitude site in Hyytiälä, Finland. The data from 2014-2018 includes particle size distributions (PSD) and their fall velocities, from which snowflake masses were derived. K- and W-band Ze values are computed using these surface-based observations and snowflake scattering properties as provided by T-matrix and single-particle scattering tables, respectively. The uncertainty analysis shows that the K-band snowfall rate estimation is significantly improved by including the intercept parameter N0 of the PSD calculated from concurrent disdrometer measurements. If N0 is used to adjust the prefactor of the Ze-S relationship, the RMSE of the snowfall rate estimate can be reduced from 0.37 to around 0.11 mmh−1. For W-band, a Ze-S relationship with constant parameters for all available snow events shows a similar uncertainty compared to the method that includes the PSD intercept parameter. To demonstrate the performance of the proposed Ze-S relationships, they are applied to measurements of the MRR and the W-band Microwave Radar for Arctic Clouds at the AWIPEV Arctic research base in Ny-Ålesund, Svalbard. The resulting snowfall rate estimates show a good agreement to in situ snowfall observations while other Ze-S relationships from literature reveal larger differences.