The aim of this study was to determine the effect of microwave power during the vacuum–microwave drying (VMD) on sour cherries in terms of drying kinetics, including the temperature profile of dried material, as well as on some quality factors of the finished product including phenolic compounds, antioxidant capacity, and color. The content of phenolic compounds, antioxidant activity, and color change were used as quality indicators of dried sour cherries. Sour cherries were dehydrated by convective drying (CD) at temperatures of 50 °C, 60 °C, and 70 °C and by VMD at the initial microwave power of 240 W, 360 W, and 480 W reduced to 240 W and 120 W in order to avoid a rapid increase in temperature at the critical moisture content of ca. 1 kg/kg dry mass. Control samples were prepared by freeze drying (FD). The increase in air temperature during CD as well as the increase in material temperature during VMD deteriorated dried product quality in terms of the content of phenolic compounds, antioxidant activity, and color, which was consistent with anthocyanins content. However, VMD turned out to be much better than CD and competitive to FD. The best quality of the dried product and its more attractive color were achieved at VMD at 480 W followed by drying at microwave power reduced to 120 W, which corresponds to anthocyanins content. In addition, the drying process had a positive impact on contents of quercetin and keampferol derivatives. Dried sour cherries have a long shelf life and therefore may be a fine alternative to fresh fruit all year round.