Arterial pressure (AP) is a crucial biomarker for cardiovascular disease prevention and management. Photoplethysmography (PPG) could provide a novel, paradigm-shifting approach for continuous, non-obtrusive AP monitoring, comfortably integrated in wearable and mobile devices; yet, it still faces challenges in accuracy and robustness. In this work, we sought to integrate machine learning (ML) techniques into a previously established, clinically-validated classical approach (oBPM®) to develop new accurate AP estimation tools based on PPG, and at the same time improve our understanding of the underlying physiological parameters. In this novel approach, oBPM® was used to pre-process PPG signals and robustly extract physiological features, and ML models were trained on these features to estimate systolic AP (SAP). A feature relevance analysis showed that reference (calibration) information, followed by various morphological parameters of the PPG pulse wave, comprised the most important features for SAP estimation. A performance analysis then revealed that LASSO-regularized linear regression, Gaussian process regression and support vector regression are effective for SAP estimation, particularly when operating on reduced feature sets previously obtained with e.g. LASSO. These approaches yielded substantial reductions in error standard deviation of 9-15% relative to conventional oBPM®. Altogether, these results indicate that ML approaches are well-suited, and promising tools to help overcoming the challenges of ubiquitous AP monitoring.