Abstract Cellular materials made from high temperature composites with efficient load supporting lattice topologies and small cell sizes would create new options for light weight, high temperature structures. A method has been developed for fabricating millimeter cell size cellular lattice structures with a square truss topology from 240 μm diameter Ti–6Al–4V coated SiC monofilaments. The compressive stiffness of the lattice structures was well approximated by that of the monofilament fraction in the loading direction. The strength of the lattices was controlled by elastic buckling and the results were accurately represented by an elastic buckling model. The post peak compressive deformation was accommodated by elastic buckling of the SiC fibers and plastic deformation of the titanium coating until the onset of monofilament fracture. The specific stiffness and strength of the lattices were found to be between 2 and 10 times that of other cellular structures and thus appear to be promising candidates for high temperature, ultralight weight load supporting applications.