The effect of polymer infiltration on the compressive strength of β-tricalcium phosphate (TCP) scaffolds fabricated by robocasting (direct write assembly) is analyzed in this work. Porous structures consisting of a tetragonal three-dimensional mesh of interpenetrating rods were fabricated from concentrated TCP inks with suitable viscoelastic properties. Biodegradable polymers (polylactic acid (PLA) and poly(ε-caprolactone) (PCL)) were infiltrated into selected scaffolds by immersion of the structure in a polymer melt. Infiltration increased the uniaxial compressive strength of these model scaffolds by a factor of three (PCL) or six (PLA). It also considerably improved the mechanical integrity of the structures after initial cracking, with the infiltrated structure retaining a significant load-bearing capacity after fracture of the ceramic rods. The strength improvement in the infiltrated scaffolds was attributed to two different contributions: the sealing of precursor flaws in the ceramic rod surfaces and the partial transfer of stress to the polymer, as confirmed by finite element analysis. The implications of these results for the mechanical optimization of scaffolds for bone tissue engineering applications are discussed.