We study spin-wave spectra of mesoscopic ferromagnetic Sierpinski carpets by means of broadband-ferromagnetic resonance measurements and micromagnetic simulations. Sierpinski carpets are self-similar fractals with noninteger Hausdorff dimension that are constructed via a deterministic iteration process. The number of quantized spin-wave modes in the spectra increases with the iteration level of the carpets and the frequency splitting resembles bandpass characteristics known from fractal antennas. We find that the splitting is sensitive to the fractal dimension as well as to the relative alignment of the magnetic field and the sides of the fractals. Micromagnetic simulations provide the localization of individual spin-wave modes determined by the confinement and the inhomogeneity of the internal field.