Modern autonomous systems often rely on LiDAR scanners, in particular for autonomous driving scenarios. In this context, reliable scene understanding is indispensable. Current learning-based methods typically try to achieve maximum performance for this task, while neglecting a proper estimation of the associated uncertainties. In this work, we introduce a novel approach for solving the task of uncertainty-aware panoptic segmentation using LiDAR point clouds. Our proposed EvLPSNet network is the first to solve this task efficiently in a sampling-free manner. It aims to predict per-point semantic and instance segmentations, together with per-point uncertainty estimates. Moreover, it incorporates methods for improving the performance by employing the predicted uncertainties. We provide several strong baselines combining state-of-the-art panoptic segmentation networks with sampling-free uncertainty estimation techniques. Extensive evaluations show that we achieve the best performance on uncertainty-aware panoptic segmentation quality and calibration compared to these baselines. We make our code available at: https://github.com/kshitij3112/EvLPSNet