Blackcurrant cultivars originating from different European countries (Finland, Latvia, Lithuania, Poland, and Scotland) but cultivated at the same geographic location and under the same climatic conditions in Finland were investigated. Berries of 21 cultivars were pressed into juices without enzymatic assistance, and the chemical and sensory profiles were studied. The genotype significantly influenced juice yield (47–70% of berry weight), anthocyanin profile (including 42–64% of delphinidins and 32–54% of cyanidins; rutinosides vs. glucosides, 3–9:1), and sensory properties of the juice (appearance, flavor, and mouthfeel). The studied cultivars exhibited a large diversity in anthocyanin content in berries (904–4595 μg/g of berries), juices (obtained by pressing pulps, 141–1028 μg/g of juices), and press residues (skins and seeds, 3492–19852 μg/g of residues). Variation of anthocyanins in juices was unrelated to the variation in berries. The perceived color was affected by the anthocyanin contents in juices but not by the anthocyanin levels in berries. These measured compounds did not have a direct association with viscosity, flavor, or aftertaste of the juices.