Using a broadband microwave spectrometer we have investigated the magnetization dynamics of mesoscopic ferromagnetic disks and rings in the frequency range from 45 MHz to 20 GHz . We studied permalloy rings with an outer diameter of 2 μ m and different ring widths w . In the mesoscopic devices we find several ferromagnetic resonance (FMR) lines which shift with the in-plane magnetic field H b . Among them, two pronounced FMR modes are identified. We attribute these modes to localized spin waves in different ring segments where the characteristic resonance frequency either decreases or increases as a function of w , depending on the orientation of the ring segment with respect to H b .