In this paper, we construct nonparametric, nonasymptotic, and simultaneous condence bands for band-limited regression functions based on the theory of Paley-Wiener kernels. We work with a sample of independent and identically distributed (i.i.d.) input-output pairs, the measurement noises are assumed to have a joint distribution that is invariant with respect to transformations from a compact matrix group (e.g., permutations), and we also assume that the distribution of the inputs is a priori known. The task is divided into two steps: rst, we study the case when the outputs are noise-free, then the problem is generalized for measurement noises. The algorithms provide nonasymptotic guarantees for the inclusion of the true regression function in the condence band, simultaneously for all possible inputs. Finally, we demonstrate our results via numerical experiments.