The roles digital media-technologies play in raising public issues relating to emerging technologies and their potential for engaging publics with science and policy assessments is a lively field of inquiry in Science and Technology Studies (STS). This paper presents an analysis of controversies over proposals for the large-scale removal of atmospheric carbon dioxide (CDR). The study combines a digital method (web-querying) with document analysis to map debates about two CDR approaches: bioenergy with carbon capture and storage (BECCS) and afforestation. In the first step, we locate actors using the web to engage with BECCS and afforestation and map their alignments in relation to competing framings of CDR. In a second step, we examine the devices deployed by UK-based actors to evidence and contest the feasibility of BECCS and afforestation. Our analysis shows that policy distinctions between “natural” and “engineered” CDR are used flexibly in practice and do not map neatly onto actor engagement with BECCS and afforestation. We highlight the predominance of cross-cutting techno-economic expertise and argue that framings of CDR as a solution to governing climate change may contribute to public disengagement from climate policy processes. The paper reflects on methods for studying controversies, publics, and issues emerging around processes of technoscientific assessment.