Circular Economy (CE) is seen as a key strategy in achieving sustainable development and the United Nations Sustainable Development Goals (SDGs). To seize the potential of CE, public and private organisations need to evaluate and communicate their progress moving away from the non-sustainable paradigm of “take–make–dispose” towards circularity. The literature and practitioners demonstrate a growing interest in CE assessment as a driver for this transition. Nevertheless, the majority of CE assessments are implemented in private companies and implementation in public sector organisations is low. This article presents the challenges that currently prevent public sector organisations from implementing CE assessment and derives strategies to overcome them. A total of 21 CE and assessment experts from the Portuguese public sector were interviewed, and the results were triangulated with an extensive policy document review. The findings show that cultural barriers, particularly a lack of public and political pressure as well as a resistance towards change, are considered the main challenges for CE assessment implementation. Cultural challenges drive structural ones such as a lack of leadership commitment, the voluntary nature, and a missing clear governance for CE assessment. Technical and financial challenges, contrary to previous findings of the literature, are not prioritised and are seen as a result of the cultural and structural challenges. Overall, the research suggests that CE assessment is often a discussion among academics and highly specialised practitioners. In order to drive its implementation, the debate has to involve stakeholders beyond expert circles to trigger awareness for its necessity and to facilitate usage for a broader audience.