We study the problem of classifier derandomization in machine learning: given a stochastic binary classifier (f: X \to [0,1]), sample a deterministic classifier (\hat{f}: X \to \{0,1\}) that approximates the output of (f) in aggregate over any data distribution. Recent work revealed how to efficiently derandomize a stochastic classifier with strong output approximation guarantees, but at the cost of individual fairness – that is, if (f) treated similar inputs similarly, (\hat{f}) did not. In this paper, we initiate a systematic study of classifier derandomization with metric fairness guarantees. We show that the prior derandomization approach is almost maximally metric-unfair, and that a simple ``random threshold’’ derandomization achieves optimal fairness preservation but with weaker output approximation. We then devise a derandomization procedure that provides an appealing tradeoff between these two: if (f) is (\alpha)-metric fair according to a metric (d) with a locality-sensitive hash (LSH) family, then our derandomized (\hat{f}) is, with high probability, (O(\alpha))-metric fair and a close approximation of (f). We also prove generic results applicable to all (fair and unfair) classifier derandomization procedures, including a bias-variance decomposition and reductions between various notions of metric fairness.