Open relation extraction (OpenRE) aims to identify relational facts within open-domain corpora without relying on predefined relation types. A significant limitation of current state-of-the-art OpenRE approaches is their inability to accurately self-assess their performance. Which is caused by the reliance on pseudo-labels, that treats all points within a cluster equally, regardless of their actual relative position according to the cluster center. This leads to models that are often overconfident in their incorrect predictions , significantly undermining their reliability. In this paper, we introduce an approach that addresses this challenge by effectively modeling a part of the epistemic uncertainty within OpenRE. Instead of using pseudo labels that mask uncertainty, our approach is built to train a classifier directly with the clustering distribution. Our experimental results across various datasets demonstrate that the suggested approach improves reliability of OpenRE by preventing overconfident errors. Furthermore we show that by improving the reliability of the predictions, UOREX operates more efficiently in a generative active learning context where an LLM is the oracle, doubling the performance gain compared to the state-of-the-art.