We have studied the ferromagnetic resonance response in a series of atomically disordered FePt thin films as a function of film thickness (9-200 nm) and excitation frequency (9.5 and 24 GHz). These films are characterized by a perpendicular anisotropy that promotes a stripelike magnetic domain structure above a critical thickness dcr~30 nm. All films display a resonant absorption due to the uniform precession of the magnetization vector. The analysis of the linewidth as a function of film thickness shows that the line broadens considerably above dcr. In the thinner films (d<28 nm) we have only observed the absorption related to the uniform precession mode, but thicker films, in which a stripe domain pattern is observed at zero field in static magnetic measurements, show an additional resonance line when the magnetic field is applied at, or very close to, the film plane normal. This line appears at fields below the main resonance and is observed at both X and K bands with approximately the same field separation from the uniform mode. We have also found that the line separation between the two resonances varies with the film thickness, indicating that the appearance of an additional resonance is related to confinement effects, but does not follow the quadratic law expected for infinite surface pinning. The ferromagnetic resonance results have been interpreted within a model of standing spin waves with finite surface pinning. From the angular variation of the pinning parameter close to the film normal we have found that the surface anisotropy is perpendicular to the film plane and increases with film thickness. The origin of the surface anisotropy seems to be related to a substrate-induced strain produced in the fabrication process and to a surface layer with a reduced magnetization. Annealing the samples at relatively low temperatures produces important changes in the resonance spectra. The overall observed behavior suggests that even though the resonance experiments are made at fields large enough to be in a magnetically saturated state, the formation of a stripe structure and the changes observed in the ferromagnetic resonance spectra above dcr are not completely uncorrelated phenomena. © 2011 American Physical Society.