The lack of meteorological observations at high latitudes and the small size and relatively short lifetime of polar lows (PLs) constitute a problem in the simulation and prediction of these phenomena by numerical models. On the other hand, PLs, which are rapidly developing, can lead to such extreme weather events as stormy waves, strong winds, the icing of ships, and snowfalls with low visibility, which can influence communication along the Arctic seas. This article is devoted to studying the possibility of the numerical simulation and prediction of polar lows by different model configurations and resolutions. The results of the numerical experiments for the Norwegian and Barents seas with grid spacings of 6.5 and 2 km using the ICON-Ru configurations of the ICON (ICOsahedral Nonhydrostatic) model and with a grid spacing of 6.5 km using the COSMO-CLM (Climate Limited-area Modeling) configuration of the COSMO (COnsortium for Small-scale MOdelling) model are presented for the cold season of 2019–2020. All the used model configurations demonstrated the possibility of the realistic simulation of polar lows. The ICON model showed slightly more accurate results for the analyzed cases. The best results showed runs with lead times of less than a day.