Fine ceramic lattices with spatial resolution <100 microm and having precise dimensions and intricate hierarchical structure are fabricated by extrusion freeforming, a rapid prototyping technique, which allows overall shape and structure to be controlled by computer. The procedure can be used for any fine ceramic powder and can therefore find applications as diverse as microwave and terahertz metamaterials (artificial crystals), hard tissue scaffolds, microfluidic devices, and metal matrix composite preforms. The examples presented here are calcium phosphate lattices with three structure levels: submicron pores, which enhance cell-surface interactions, pores of tens of microns to encourage bone ingrowth, and corridors (hundreds of microns) for vascularization. With controlled pore structures on these scales, the lattices are expected to provide customized biological, mechanical, and geometrical requirements.