This dataset provides an overview of the current state of research assessment practices related to Open Research Data (ORD) within Swiss Higher Education Institutions (HEIs). The goal of this analysis is to delineate existing practices, requirements, and obstacles in assessing ORD across three levels: research proposals, individual researchers, and research units or institutions, depending on their administrative structures. The online survey was distributed to all Swiss universities, federal institutes of technology, universities of applied sciences, and universities of teacher education, according to the swissuniversities list from 2024. The survey focused on formalised research assessment practices and ORD policies and support.