Since the 2000s, Business Process Management (BPM) has evolved into a comprehensively studied discipline that goes beyond the boundaries of particular business processes. By also affecting enterprise-wide capabilities (such as an organisational culture and structure that support a process-oriented way of working), BPM can now correctly be called Business Process Orientation (BPO). Meanwhile, various maturity models have been developed to help organisations adopt a process-oriented way of working based on step-by-step best practices. The present article reports on a case study in which the process portfolio of an organisation is assessed by different maturity models that each cover a different set of process-oriented capabilities. The purpose is to reflect on how business process maturity is currently measured, and to explore relevant considerations for practitioners, scholars and maturity model designers. Therefore, we investigate a possible difference in maturity scores that are obtained based on model-related characteristics (e.g. capabilities, scale and calculation technique) and respondent-related characteristics (e.g. organisational function). For instance, based on an experimental design, the original maturity scores are recalculated for different maturity scales and different calculation techniques. Follow-up research can broaden our experiment from multiple maturity models in a single case to multiple maturity models in multiple cases.