Current methods for transcutaneous blood gas monitoring (TBM) - a common health monitoring method in neonatal care - comes with a suite of challenges like limited attachment opportunities, and risks of infections from burning and tearing of the skin, which limits its use. This study presents a novel system and method for rate-based transcutaneous CO2 measurements with a soft, unheated skin-interface that can address many of these problems. Additionally, a theoretical model for the gas transport from the blood to the system's sensor is derived. By simulating CO2 advection and diffusion through the cutaneous microvasculature and epidermis to the system's skin interface, the effect of a wide range of physiological properties on the measurement has been modeled. Following these simulations, a theoretical model for the relationship between the measured CO2 concentration and that in the blood was derived and compared to empirical data. Applying the model on measured blood gas levels, even when the theory was based solely on the simulations, produced blood CO2 concentrations within ∼35% of empirical measurements from a state-of-the-art device. Further calibration of the framework, also using the empirical data, yielded an output with a Pearson correlation of 0.84 between the two methods. Compared to the state-of-the-art device the proposed system measured the partial CO2 pressure in the blood with an average deviation of 0.04 kPa and 1.97σ of ±1.1 kPa. However, the model indicated that this performance could be hampered by different skin properties. Given its soft and gentle skin interface and lack of heating, the proposed system could significantly decrease health risks like, burns, tears, and pain, currently associated with TBM on premature neonates.