Uncertainty Quantification (UQ) is an important building block for the reliable use of neural networks in real-world scenarios, as it can be a useful tool in identifying faulty predictions. Speech emotion recognition (SER) models can suffer from particularly many sources of uncertainty, such as the ambiguity of emotions, Out-of-Distribution (OOD) data or, in general, poor recording conditions. Reliable UQ methods are thus of particular interest as in many SER applications no prediction is better than a faulty prediction. While the effects of label ambiguity on uncertainty are well documented in the literature, we focus our work on an evaluation of UQ methods for SER under common challenges in real-world application, such as corrupted signals, and the absence of speech. We show that simple UQ methods can already give an indication of the uncertainty of a prediction and that training with additional OOD data can greatly improve the identification of such signals.