Optical limiting by suspensions of Au nanoparticles is enhanced by several orders of magnitude with the use of complex plasmonic shapes, such as spined "nanourchins," instead of nanospheres. Similar enhancements are observed by changing the material of nanospheres from Au to Ag. The experiments, measuring intensity-dependent transmission over a wavelength range from 450 to 650 nm for a 6 ns pulsed laser, are analyzed in terms of an effective nonlinear extinction coefficient, which we relate to the local, plasmonically enhanced electric field. FDTD simulations reveal a large electric field enhancement inside the nanospined structures and qualitatively confirm the plasmonic trends, where Ag nanospheres and Au nanourchins are more effective than Au nanospheres. These results suggest that designing nanostructures for the maximum plasmonic enhancement provides a roadmap to materials and geometries with optimized optical limiting behavior.