In this study, solid olive mill waste (SOMW) was used to obtain antioxidant compounds using solid–liquid extraction. The effect of different extraction methods, namely microwave-assisted extraction (MAE), ultrasound-assisted extraction (UAE), Soxhlet, and conventional solvent extraction, on the yield, total phenolics, and total antioxidant activity of SOMW extracts was investigated. Untreated and dried SOMW were subjected to extraction with water and methanol. The antioxidant activity of the extracts was evaluated using the DPPH assay, while their total phenolic content was measured using the Folin–Ciocalteu method. For the characterisation of the extracts, HPLC-DAD analysis was performed. The results showed that the extraction yield was significantly influenced (p < 0.05) by the solvent used, the material treatment prior to extraction, the moisture content of SOMW samples, and the extraction time. The optimised parameters were water, as the extraction solvent, and MAE as the extraction technique (extraction temperature of 50 °C and time of 1 h). The evaluation of the antioxidant activity of the extracts indicated that phenolics were the dominant bioactive compounds. The extracts were found to be rich in several hydroxytyrosol derivatives. Therefore, SOMW can be a valuable resource for bioactive compounds using conventional and innovative extraction techniques.