Radar sensors are crucial for environment perception of driver assistance systems as well as autonomous cars. Key performance factors are a fine range resolution and the possibility to directly measure velocity. With a rising number of radar sensors and the so far unregulated automotive radar frequency band, mutual interference is inevitable and must be dealt with. Sensors must be capable of detecting, or even mitigating the harmful effects of interference, which include a decreased detection sensitivity. In this paper, we evaluate a Convolutional Neural Network (CNN)-based approach for interference mitigation on real-world radar measurements. We combine real measurements with simulated interference in order to create input-output data suitable for training the model. We analyze the performance to model complexity relation on simulated and measurement data, based on an extensive parameter search. Further, a finite sample size performance comparison shows the effectiveness of the model trained on either simulated or real data as well as for transfer learning. A comparative performance analysis with the state of the art emphasizes the potential of CNN-based models for interference mitigation and denoising of real-world measurements, also considering resource constraints of the hardware.