Self-supervised learning (SSL) is an effective method for exploiting unlabelled data to learn a high-level embedding space that can be used for various downstream tasks. However, existing methods to monitor the quality of the encoder -- either during training for one model or to compare several trained models -- still rely on access to annotated data. When SSL methodologies are applied to new data domains, a sufficiently large labelled dataset may not always be available. In this study, we propose several evaluation metrics which can be applied on the embeddings of unlabelled data and investigate their viability by comparing them to linear probe accuracy (a common metric which utilizes an annotated dataset). In particular, we apply $k$-means clustering and measure the clustering quality with the silhouette score and clustering agreement. We also measure the entropy of the embedding distribution. We find that while the clusters did correspond better to the ground truth annotations as training of the network progressed, label-free clustering metrics correlated with the linear probe accuracy only when training with SSL methods SimCLR and MoCo-v2, but not with SimSiam. Additionally, although entropy did not always have strong correlations with LP accuracy, this appears to be due to instability arising from early training, with the metric stabilizing and becoming more reliable at later stages of learning. Furthermore, while entropy generally decreases as learning progresses, this trend reverses for SimSiam. More research is required to establish the cause for this unexpected behaviour. Lastly, we find that while clustering based approaches are likely only viable for same-architecture comparisons, entropy may be architecture-independent.