Alloys from the CoCrFeMnNi family remain the most studied austenitic high-entropy alloys. In this study, four alloys, i.e., Cantor alloy, A3S (modified nonequiatomic Cantor composition), both “pure” or doped with carbon (200 wt. ppm) and niobium (1.3 wt.%), were investigated. Firstly, alloys were induction cast using a cold-crucible method. The obtained ingots were molten, and rapidly solidified by melt-spinning at two cooling rates to obtain “ribbons”, typical of such processing. The effects of the solidification rate and the presence of carbon and niobium on the microstructure and hardness were studied. All the studied alloys show an fcc structure. The lattice parameter of the fcc phase increases with the increasing cooling rate, and with the addition of niobium and carbon, which confirms at least a partial presence of these elements in solid solution. Yet, TEM observations revealed the formation of nanometric NbC precipitates. The microstructure of melt-spun ribbons consists of equiaxed grains of a few micrometers in size. The higher cooling rate led to a small decrease in the grain size and a slight increase in hardness. Moreover, the hardness of doped alloys can be further improved by annealing (500°C for 24 h) through NbC precipitation.