Assessing Earth system responses arising from carbon dioxide removal (CDR) requires developing and simulating pairs of scenarios – a mitigation scenario with deployment of CDR and a corresponding no-CDR baseline. The latter describes a world where no CDR is deployed, such that net carbon emissions are higher and a given temperature target may be missed. While over the past years a rich literature on deep mitigation scenarios with CDR has been emerging, no-CDR baselines have mostly been explored in stylized Earth system model (ESM) experiments. In such simulations, a no-CDR baseline simply assumes that CDR is “switched off”, while socio-economic constraints are not considered. However, the deployment of CDR in deep mitigation scenarios, created by integrated assessment models (IAMs), is embedded in a consistent socio-economic description of plausible futures, and disallowing CDR may affect climate drivers due to changes in the energy system and in land-use dynamics. Particularly, when moving towards an activity-driven representation of CDR in emission-driven ESMs, where the activity that draws down CO₂ from the atmosphere is explicitly modelled, the creation of no-CDR baselines comes with challenges and trade-offs. Here, we conceptualize a framework for emission-driven ESM simulations of IAM scenarios that allows us to determine carbon-cycle and biogeophysical feedbacks of CDR deployment using no-CDR baselines. We show that different options exist for the creation of no-CDR baselines, which offer different insights and have their specific advantages and limitations. We also demonstrate that internal variability of the climate system inherently limits our ability to detect the small signals related to CDR deployment and its feedbacks. Hence, unless a sufficiently large initial conditions ensemble is employed, stylized modelling approaches may remain preferable for some applications, e.g., the quantification of regional biogeophysical effects of CDR deployment.