The measurement of the absolute rate of cerebral metabolic oxygen consumption (CMRO2) is likely to offer a valuable biomarker in many brain diseases and could prove to be important in our understanding of neural function. As such there is significant interest in developing robust MRI techniques that can quantify CMRO2 non-invasively. One potential MRI method for the measurement of CMRO2 is via the combination of fMRI and cerebral blood flow (CBF) data acquired during periods of hypercapnic and hyperoxic challenges. This method is based on the combination of two, previously independent, signal calibration techniques. As such analysis of the data has been approached in a stepwise manner, feeding the results of one calibration experiment into the next. Analysing the data in this manner can result in unstable estimates of the output parameter (CMRO2), due to the propagation of errors along the analysis pipeline. Here we present a forward modelling approach that estimates all the model parameters in a one-step solution. The method is implemented using a regularized non-linear least squares approach to provide a robust and computationally efficient solution. The proposed framework is compared with previous analytical approaches using modelling studies and in vivo acquisitions in healthy volunteers (n = 10). The stability of parameter estimates is demonstrated to be superior to previous methods (both in vivo and in simulation). In vivo estimates made with the proposed framework also show better agreement with expected physiological variation, demonstrating a strong negative correlation between baseline CBF and oxygen extraction fraction. It is anticipated that the proposed analysis framework will increase the reliability of absolute CMRO2 measurements made with calibrated BOLD.