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Electrodermal activity (EDA) is a biosignal that contains valuable information for monitoring health conditions related to sympathetic nervous system activity. Analyzing ambulatory EDA data is challenging because EDA measurements tend to be noisy and sparsely labeled. To address this problem, we present the first study of contrastive learning that examines approaches that are tailored to the EDA signal. We present a novel set of data augmentations that are tailored to EDA, and use them to generate positive examples for unsupervised contrastive learning. We evaluate our proposed approach on the downstream task of stress detection. We find that it outperforms baselines when used both for fine-tuning and for transfer learning, especially in regimes of high label sparsity. We verify that our novel EDA-specific augmentations add considerable value beyond those considered in prior work through a set of ablation experiments.