Recent advances in multiscale manufacturing enable fabrication of hollow-truss based lattices with dimensional control spanning seven orders of magnitude in length scale (from ;50 nm to ;10 cm), thus enabling the exploitation of nano-scale strengthening mechanisms in a macroscale cellular material. This article develops mechanical models for the compressive strength of hollow microlattices and validates them with a selection of experimental measurements on nickel microlattices over a wide relative density range (0.01–10%). The limitations of beam-theory-based analytical approaches for ultralight designs are emphasized, and suitable numerical (finite elements) models are presented. Subsequently, a novel computational platform is utilized to efficiently scan the entire design space and produce maps for optimally strong designs. The results indicate that a strong compressive response can be obtained by stubby lattice designs at relatively high densities (~10%) or by selectively thickening the nodes at ultra-low densities.