Fluorescence microscopy is a major driver of scientific progress in the life sciences. Although high-end confocal microscopes are capable of filtering out-of-focus light, cheaper and more accessible microscopy modalities, such as widefield microscopy, can not, which consequently leads to hazy image data. Computational dehazing is trying to combine the best of both worlds, leading to cheap microscopy but crisp-looking images. The perception-distortion trade-off tells us that we can optimize either for data fidelity, e.g. low MSE or high PSNR, or for data realism, measured by perceptual metrics such as LPIPS or FID. Existing methods either prioritize fidelity at the expense of realism, or produce perceptually convincing results that lack quantitative accuracy. In this work, we propose HazeMatching, a novel iterative method for dehazing light microscopy images, which effectively balances these objectives. Our goal was to find a balanced trade-off between the fidelity of the dehazing results and the realism of individual predictions (samples). We achieve this by adapting the conditional flow matching framework by guiding the generative process with a hazy observation in the conditional velocity field. We evaluate HazeMatching on 5 datasets, covering both synthetic and real data, assessing both distortion and perceptual quality. Our method is compared against 12 baselines, achieving a consistent balance between fidelity and realism on average. Additionally, with calibration analysis, we show that HazeMatching produces well-calibrated predictions. Note that our method does not need an explicit degradation operator to exist, making it easily applicable on real microscopy data. All data used for training and evaluation and our code will be publicly available under a permissive license.