The topic of automated driving is receiving increasing attention from the scientific community and automotive industry. A key task for an autonomous vehicle is the recognition of drivable area and, in an extension of this, detecting the road boundaries. State-of-the-art techniques often use camera and/or LIDAR sensors to perform this task. However, these sensors can be expensive and not suitable in low visibility situations such as during nighttime or in bad weather. Radar sensors are a viable alternative. The aims of this study are twofold: to introduce a technique of radar-based road boundary estimation (RBE) using radar sensors and to develop a suitable benchmark to compare different radar-based RBE techniques. The RBE algorithm proposed in this study, Clustering-based Urban Road Boundary Estimation (CURBE), clusters the radar detections and incorporates domain knowledge to determine which of the clusters describe road boundaries (so-called boundary clusters). Additionally, we propose a novel benchmark to compare radar RBE algorithms. The benchmark makes use of the nuScenes data set. Each radar reflection in the data set is given a ground truth label. The radar reflection is given the label of boundary point or non-boundary point based on several sources such as the measured radial velocity, object annotations, and a detailed road map. To quantify the performance of an RBE algorithm, the estimated labels outputted by the RBE algorithm are compared to the ground truth labels using the metrics precision, recall, and F1-score. CURBE is evaluated on the benchmark where it achieves an F1-score of 30.4%. We conclude that with the current version of CURBE and with the current method of measuring performance there are not enough grounds to consider this method as a reliable way of RBE. However, the approach shows promise. The method has the potential to significantly improve performance by using a clustering method that is designed for radar data or implementing a different way of selecting boundary clusters. Since the proposed benchmark uses the radar reflections in the data set as ground truth the performance measurement is less accurate in recordings with limited radar coverage, but overall it is concluded that the benchmark provides a fast and consistent way to measure and compare the performance of different RBE algorithms.