We consider, in the frame of the long-wavelength Heisenberg model, the effect of a pinning field on the spin wave band gaps and transmission spectra of one-dimensional comb-like structures. Using a Greens function method, we obtained closed-form expressions for the band structure and the transmission coefficients for an arbitrary value of the number N of sites (Nof resonators) in the comb-like structure. We report the opening-up of stop bands inside the pass-bands due to the effect of the pinning field at the ends of the resonators of the comb. These structures, composed of one-dimensional ferromagnetic materials, may exhibit large gaps where the propagation of spin waves is forbidden. The width and frequency position of these gaps depends on the strength of the pinning field.