In the last years, the circular economy (CE) paradigm is being widely explored by researchers and institutions as a possible path to increase the sustainability of our economic system. Reuse, repair and recycling are becoming crucial activities in many sectors. At the same time, companies are showing an increasing interest for this new economic model. However, the state of the art shows that a deep research on CE assessment and indicators is still lacking, in particular on the micro level. This work tries to fill this gap, first analyzing the current literature on CE assessment, then proposing a reference framework for the monitoring phase of a CE strategy. Finally, the main existing environmental assessment methodologies based on indexes are analyzed according to their suitability to evaluate the circularity of a system. A systematic approach for the choice of the adequate methodology is also provided, highlighting the main critical steps in the assessment of a CE strategy. Further research could be focused either on the extension of this approach to include other assessment methods, and on the validation of this proposal in a case study.