The disclosed structure is configured such that it does not support electromagnetic waves having frequencies within a selected band gap; those electromagnetic waves are thus reflected. Some variations provide an omnidirectional infrared reflector comprising a three-dimensional photonic crystal containing: rods of a first material that has a first refractive index, wherein the rods are arranged to form a plurality of lattice periods in three dimensions, and wherein the rods are connected at a plurality of nodes; and a second material that has a refractive index that is lower than the first refractive index, wherein the rods are embedded in the second material. The lattice spacing and the rod radius or width are selected to produce a photonic band gap within a selected band of the infrared spectrum. Methods of making and using the three-dimensional photonic crystal are described. Applications include thermal barrier coatings and blackbody emission signature control.