Problems framed as societal challenges have provided fresh impetus for transdisciplinary research. In response, funders have started programmes aimed at increasing transdisciplinary research capacity. However, current programme evaluations do not adequately measure the skills and characteristics of individuals and collectives doing this research. Addressing this gap, we propose a systematic framework for evaluating transdisciplinary research based on the Capability Approach, a set of concepts designed to assess practices, institutions, and people based on public values. The framework is operationalized through a mixed-method procedure which evaluates capabilities as they are valued and experienced by researchers themselves. The procedure is tested on a portfolio of 'pump-priming' research projects in the UK. We find these projects are sites of capability development in three ways: through convening cognitive capabilities required for academic practice; cultivating informal tacit capabilities; and maintaining often unacknowledged backstage capabilities over durations that extend beyond the lifetime of individual projects. Directing greater attention to these different modes of capability development in transdisciplinary research programmes may be useful formatively in identifying areas for ongoing project support, and also in steering research system capacity towards societal needs.