Nigella sativa L. seeds and their industrial process products, oils, cake, and meal, are valuable sources of bioactive compounds with antioxidant properties. In this work, the effect of technological processes on the antioxidant capacity (AC) and total phenolic content (TPC) in the black cumin oils obtained by cold pressing and solvent extraction, as well as the by-products, were evaluated. The AC values of black cumin seeds (BCS), cold-pressed black cumin oil (BCCPO), black cumin oil extracted from seeds (BCEO-S), black cumin oil extracted from cake (BCEO-C), black cumin cake (BCC), and black cumin meal (BCM) were determined by 2,2-diphenyl-1-picrylhydrazyl (DPPH) and cupric reducing antioxidant capacity (CUPRAC) assays, whereas TPC in these samples was analyzed by the Folin–Ciocalteu (FC) method. Two applied conventional oil extraction methods, screw pressing and solvent extraction, significantly affected the AC and TPC in the obtained black cumin oils and by-products. The solvent-extracted black cumin oils revealed higher antioxidant properties (DPPH = 4041–16,500 μmol TE/100 g, CUPRAC = 1275–4827 μmol TE/100 g) than the cold-pressed black cumin oil (DPPH = 3451 μmol TE/100 g and CUPRAC = 3475 μmol TE/100 g). In addition, the oil yield (20.92–48.86%) and antioxidant properties of BCCPO (DPPH = 2933–5894 μmol TE/100 g and TPC = 135–199 mg GAE/100 g) and BCC (DPPH = 1890–2265 μmol TE/100 g and TPC = 284–341 mg GAE/100 g) closely depended on the nozzle diameters (5, 8, and 10 mm) mounted in a screw press. Although both by-products were a rich source of antioxidants, BCM had significantly lower CUPRAC (1514 μmol TE/100 g) and TPC (92 mg GAE/100 g) values than BCC (CUPRAC = 3397 μmol TE/100 g and TPC = 426 mg GAE/100 g). Nevertheless, acid hydrolysis and alkaline hydrolysis of BCM extracts significantly increased their antioxidant potential. However, the DPPH (35,629 μmol TE/100 g), CUPRAC (12,601 μmol TE/100 g), and TPC (691 mg GAE/100 g) results were higher for the BCM extract after acid hydrolysis than those for alkaline hydrolysate (DPPH = 2539 μmol TE/100 g, CUPRAC = 5959 μmol TE/100 g, and TPC = 613 mg GAE/100 g). Finally, the generated AGREEprep metrics highlighted the sustainability and the greenness of the cold pressing of oil from BCS.