Bioactive peptides (BAPs) can be derived from a variety of sources; these could be from dietary proteins which are then broken down in the gastrointestinal tract to release BAPs, or they can be isolated from various sources ex vivo. Sources include plant-based proteins such as soy, and chickpeas, and animal proteins from waste from the meat industry and from fish skin. Bioinformatics is also a useful approach to assess the peptides released from digests due to the great number of possible sequences that can be isolated from proteins. Therefore, an in silico analysis of peptides could potentially lead to a more rapid discovery of BAPs. This article investigates a “crude” liver peptide mixture derived from papain hydrolysis of porcine liver and purified peptides derived from the hydrolysates following HPLC fractionation and in silico digestion of the host proteins identified using LC-MS/MS. This allowed the identification of two proteins (cytosol aminopeptidase and haemoglobin subunit alpha) present in the “crude” mixture after LC-MS/MS. In silico hydrolysis of these proteins identified that several peptides were predicted to be both present in the crude mixture using the BIOPEP database and to have potential bioactivity using the Peptide Ranker tool. Peptides (FWG, MFLG and SDPPLVFVG) with the greatest potential bioactivity and which had not previously been reported in the literature were then synthesised. The results indicated that the predicted bioactivity of the synthetic peptides would likely include antioxidant activity. FWG and MFLG derived from the in silico papain hydrolysis of cytosol aminopeptidase showed activity better or comparable to Trolox in the Oxygen Radical Absorbance Capacity (ORAC) assay. The use of these in silico tools, alongside a robust range of biochemical assays which cover a wider range of bioactivities would be a way of improving the discovery of novel bioactive peptides.