Self-supervised learning (SSL) has proven effective in learning high-quality representations for various downstream tasks, with a primary focus on semantic tasks. However, its application in geometric tasks remains underexplored, partially due to the absence of a standardized evaluation method for geometric representations. To address this gap, we introduce a novel pose-estimation benchmark for assessing SSL geometric representations, which demands training without semantic or pose labels and achieving proficiency in both semantic and geometric downstream tasks. On this benchmark, we study enhancing SSL geometric representations without sacrificing semantic classification accuracy. We find that leveraging mid-layer representations improves pose-estimation performance by 10-20%. Further, we introduce an unsupervised trajectory-regularization loss, which improves performance by an additional 4% and improves generalization ability on out-of-distribution data. We hope the proposed benchmark and methods offer new insights and improvements in self-supervised geometric representation learning.