The novelty of EDM machining as a drilling operation for composite materials means that there is no consensus on the influence of the parameters that optimise the final quality. For these reasons, a characterisation of the EDM drilling process of a unidirectional composite material has been developed. The influence of several cutting parameters has been related to the quality of the final hole obtained. Thus, macrogeometric aspects in terms of conicity and final diameter and microgeometric aspects in terms of surface quality have been evaluated. In addition, the final state of the material and the wear of the electrode have been evaluated by visual inspection, allowing the range of cutting parameters that offer the best performance to be established. Finally, a series of contour diagrams based on predictive models have been obtained to establish a direct relationship between input and output variables.