Object type classification for automotive radar has greatly improved with recent deep learning (DL) solutions, however these developments have mostly focused on the classification accuracy. Before employing DL solutions in safety-critical applications, such as automated driving, an indispensable prerequisite is the accurate quantification of the classifiers' reliability. Unfortunately, DL classifiers are characterized as black-box systems which output severely over-confident predictions, leading downstream decision-making systems to false conclusions with possibly catastrophic consequences. We find that deep radar classifiers maintain high-confidences for ambiguous, difficult samples, e.g. small objects measured at large distances, under domain shift and signal corruptions, regardless of the correctness of the predictions. The focus of this article is to learn deep radar spectra classifiers which offer robust real-time uncertainty estimates using label smoothing during training. Label smoothing is a technique of refining, or softening, the hard labels typically available in classification datasets. In this article, we exploit radar-specific know-how to define soft labels which encourage the classifiers to learn to output high-quality calibrated uncertainty estimates, thereby partially resolving the problem of over-confidence. Our investigations show how simple radar knowledge can easily be combined with complex data-driven learning algorithms to yield safe automotive radar perception.