Raspberry fruit pomace, a byproduct of juice production, was studied as a potential source of antioxidant compounds. Target high-performance liquid chromatography analysis of important polyphenolic compounds (gallic, p-coumaric, caffeic, quercitrin, chlorogenic, and ellagic acid) was performed together with analysis of total phenolic content (TPC), total flavonoid content (TFC), total anthocyanins content (TAC), and antioxidant capacity (via ferric reducing antioxidant power (FRAP) and 1,1-diphenyl-2-picrylhydrazyl (DPPH) assays). The differences in polyphenolic content of Rubus idaeus L. pomace were evaluated following ultrasound-assisted extraction and conventional maceration with different organic solvents. Additionally, the yield of free phenolics was measured in hydrolyzed pomace extracts. The results obtained show that the ultrasound method maximizes the quantity of antioxidant compounds in terms of TPC (27.79 mg/L gallic acid equivalent (GAE)), TFC (8.02 mg/g quercetin equivalent (QE)), TAC (7.13 mg/L cyanidine-3-glucoside equivalent (C3G Eq)), caffeic (19.17 µg/g), chlorogenic (3.56 µg/g), ellagic (105.52 µg/g), and gallic acids (8.75 µg/g), as well as FRAP (1002.72 µmol/L) and DPPH assays (969.71 µmol/mL vitamin C equivalent (vit C Eq); 567.00 µmol/100 g Trolox equivalent (TE)). On the other hand, conventional maceration maximizes the yield of quercetin and p-coumaric acid. In terms of biowaste valorization, raspberry fruit pomace has a promising industrial potential and may prove to be useful in the development of antioxidant dietary supplements.