In (self-)supervised (pre-)training, such as in contrastive learning, often a network is presented with correspondent (positive) and non-correspondent (negative) pairs of datapoints, and is trained to find an embedding vector for each datapoint, i.e., a representation, which can be further fine-tuned for various downstream tasks. To safely deploy these models in critical decision-making systems, it is crucial to equip them with a measure of their reliability. Here we study whether such measures can be quantified for a datapoint in a meaningful way. In other words, we explore if the downstream performance on a given datapoint is predictable, directly from a few characteristics of its pre-trained embedding.We study whether this goal can be achieved by directly estimating the distribution of the training data in the embedding space, and accounting for the local consistency of the representations. Our experiments show that these notions of reliability often strongly correlate with its downstream accuracy.