Change detection is an important data processing task in remote sensing, with applications such as deforestation monitoring or natural disaster assessment. Synthetic Aperture Radar (SAR) imaging offers key advantages for change detection, in particular due to its robustness to weather condition and cloud coverage. Because of the speckle phenomenon, the intensity of SAR images suffer from strong fluctuations, making the detection of radiometric changes challenging. Our method builds on a recently introduced self-supervised despeckling technique. It estimates despeckling uncertainty to better identify meaningful differences between two despeckled images. Conformal prediction permits to approach the change detection problem from the angle of anomaly detection. Thus, we develop a fully unsupervised change detection approach with a controlled probability of false alarm. Experimental results on TerraSAR-X satellite images with metric resolution show the capability of our method to detect changes without any supervision.