Abrasive waterjet cutting is a manufacturing technology making use of a high-speed waterjet with abrasive particles in suspension, for cutting materials with different mechanical properties. Product quality requirements are pushing towards an improvement of tracking and stabilization methods of the relevant process variables. Amongst those, the jet kinetic power defines the cutting capability and has a significant impact on the final cut features. This variable is subject to relevant fluctuations versus time. Besides, the current state of the art does not provide means for its in-line monitoring. The aim of this contribution is to monitor the airborne acoustic emission of an abrasive waterjet cutting head and investigate its correlation with the jet kinetic power. The investigation is carried out by means of factorial studies, in which the jet is fired at various water pressures and abrasive feed rates, providing different kinetic powers. The acoustic emission is synchronously monitored by means of a condenser microphone, installed on the cutting head. Data at frequencies above 40 kHz is found to constitute a robust and selective acoustic signature of the airborne jet. The acoustic signature is proven to be an effective in-line indicator of the jet kinetic power and its pressure-induced variations, whilst abrasive-induced variations remain undetected. A calibration procedure is presented, for translating the acoustic data into a jet kinetic power. The method is validated by means of further experiments that envisage its deployment in a real scenario. Overall, the presented method constitutes a robust tool for monitoring pressure-induced variations of the jet cutting capability.