Safety-critical systems in domains such as aerospace, railways, and automotive require anomaly detection methods that are not only accurate but also transparent, predictable, and certifiable under strict operational constraints. Traditional deep neural networks fall short in these contexts because their black-box nature prevents formal reasoning, and their outputs cannot be restricted within well-defined operational limits. In this paper, we present SafeKAN, developed in collaboration with Thales Alenia Space, to address anomaly detection in satellite telemetry. SafeKAN builds on Kolmogorov–Arnold Networks (KANs) and introduces domain-specific adaptations, including codomain bounds derived from noise statistics, the exploitation of periodicity to learn from minimal datasets, and the estimation of signal period without prior knowledge. The results show that SafeKAN can achieve reliable anomaly detection while operating within safety bounds and providing the transparency required in certification processes.