Internationally, there has been a push for the prioritisation of research impact beyond its scholarly contribution. Traditionally, research impact assessments have focused on academic impact and quantitative measures, at the expense of researchers for whom research impact cannot be quantified. Bibliometric indicators and other quantitative measures are still the most widely used method for evaluating research impact because these measures are easy to use and provide a quick solution for evaluators. Conversely, metric indicators fail to capture important dimensions of high-quality research. Hence, in this study, we explored challenges with metric indicators. We adopted a case study of the University of Cape Town and used document analysis, a questionnaire survey to collect data from academics and researchers, as well as semi-structured interviews with a sample of academic and research staff. The findings highlight common challenges with quantitative measures, such as bias and discipline coverage, and the ability of measures to drive researchers’ behaviour in another direction. We propose the adoption of responsible research metrics and assessment in South African higher education institutions for more inclusive and equitable research impact assessments.