In global climate governance, anticipatory assessments map future options and pathways, in light of prospective risks and uncertainties, to inform present-day planning. Using data from 125 interviews, we ask: How are foundational experts contesting the conduct of anticipatory assessment of carbon removal and solar geoengineering – as two emerging but controversial strategies for engaging with climate change and achieving Net Zero targets? We find that efforts at carbon removal and solar geoengineering assessment leverage and challenge systems modeling that has become dominant in mapping and communicating future climate impacts and mitigation strategies via IPCC reports. Both suites of climate intervention have become stress-tests for the capacity of modeling to assess socio-technical strategies with complex, systemic dimensions. Meanwhile, exploring societal dimensions demands new modes of disciplinary expertise, qualitative and deliberative practices, and stakeholder inclusion that modelling processes struggle to incorporate. Finally, we discuss how the patterns of expert contestation identified in our results speak to multiple fault-lines within ongoing debates on reforming global environmental assessments, and highlights key open questions to be addressed. © 2022 The Authors