Quantization and pruning are fundamental approaches for model compression, enabling efficient inference for language models. In a post-training setting, state-of-the-art quantization and pruning methods require calibration data, a small set of unlabeled examples. Conventionally, randomly sampled web text is used, aiming to reflect the model training data. However, this poses two key problems: (1) unrepresentative calibration examples can harm model performance, and (2) organizations increasingly avoid releasing model training data. In this paper, we propose self-calibration as a solution. Our approach requires no external data, instead leveraging the model itself to generate synthetic calibration data as a better approximation of the pre-training data distribution. We extensively compare the performance of self-calibration with several baselines, across a variety of models, compression methods, and tasks. Our approach proves consistently competitive in maximizing downstream task performance, frequently outperforming even using real data.