When it comes to preserving privacy in medical machine learning, two important considerations are (1) keeping data local to the institution and (2) avoiding inference of sensitive information from the trained model. These are often addressed using federated learning and differential privacy, respectively. However, the commonly used Federated Averaging algorithm requires a high degree of synchronization between participating institutions. For this reason, we turn our attention to Private Aggregation of Teacher Ensembles (PATE), where all local models can be trained independently without inter-institutional communication. The purpose of this paper is thus to explore how PATE -- originally designed for classification -- can best be adapted for semantic segmentation. To this end, we build low-dimensional representations of segmentation masks which the student can obtain through low-sensitivity queries to the private aggregator. On the Brain Tumor Segmentation (BraTS 2019) dataset, an Autoencoder-based PATE variant achieves a higher Dice coefficient for the same privacy guarantee than prior work based on noisy Federated Averaging.