The antioxidant capacity (AC) of rapeseed, white flakes, and meal was determined by the novel cerium oxide nanoparticle-based (CeONP) method and a previously described assay based on the formation of silver nanoparticles (AgNP). Antioxidants present in rapeseed and its by-product extracts reduced cerium(IV) ions to red-purple solutions of cerium oxide nanoparticles at pH 5.6. The influences of time, temperature, pH, and the concentration of the cerium(IV) sulfate solution on cerium oxide nanoparticle generation were estimated. The average AC of the studied extracts of real samples ranged between 1037 and 3012 μmol sinapic acid (SA) 100 g−1 and 3859–12,534 μmol SA 100 g−1 for CeONP and AgNP assays, respectively. There is significant, positive correlation between the AC of the examined extracts determined by both analytical methods (r = 0.8189). Satisfactory values of relative standard deviation (RSD = 1.2–3.9 %) and recovery (95.8–103.3 %) demonstrate a good precision and accuracy of the novel CeONP method for the AC analysis of rapeseed and its by-products.