The static and dynamic behavior of Ni80Fe20 anti-ring arrays has been systematically investigated using broadband ferromagnetic resonance (FMR) spectroscopy, magneto-optical Kerr effect (MOKE), and magnetic force microscopy (MFM). The unit cell of this periodic lattice represents a hole in a continuous film, with an elliptical nanodot placed in the middle of the hole. The FMR responses display multiple absorption peaks due to the superposition of the absorptions from the anti-dot and the central nanomagnet (dot) regions of the anti-ring structures. Interestingly, for fixed anti-ring geometry, the static and dynamic behavior is markedly sensitive to the thickness of the structure due to complicated spatial distributions of the demagnetizing field. Direct MFM imaging reveals that at remanence, the central nanomagnets are in a single-domain state, for small sample thicknesses, whereas for larger thicknesses, they display a multidomain or vortex state. This observation is in good agreement with both FMR and MOKE data. All our results agree well with micromagnetic simulations. © 2013 American Physical Society.