The energy efficiency of optoelectronic components and devices is critically dependent on minimizing undesired reflections from interfaces between materials with differing optical properties. Antireflection coatings based on metamaterials with deep-subwavelength features offer superior performance over their homogeneous counterparts as they afford subtle tuning of the refractive index and gradients therein. Recent work also showed that arrays of larger-sized (250 nm diameter), high-index nanostructures placed on semiconductor surfaces reduce the reflectivity by capitalizing on optical Mie resonances. Here, we start by demonstrating that a judiciously designed, single Mie resonator can enable perfect, local antireflection at its resonance frequency. This insight opens the door to the development of entirely new, multiresonant antireflection coating (ARC) designs in which differently sized Mie resonators manage antireflection at different wavelengths. We demonstrate the value of such multiresonant ARCs for solar applications by showing an average reflectivity as low as 4% from a silicon wafer across the visible range.