The fracture toughness of highly-ordered multi-wall carbon-nanotube-reinforced alumina composites is calculated from experimental data on nanoindentation cracking. A combined analytical and numerical model, using cohesive zone models for both matrix cracking and nanotube crack bridging and accounting for residual stresses, is developed to interpret the indentation results and evaluate the fracture toughness of the composite. Results show that residual stress and nanotube bridging play important roles in the nanocomposite fracture. The contribution to toughness from the nanotube bridging for cracking transverse to the axis of the nanotubes is calculated to be similar to5 MPa-m(1/2). From the nanotube bridging law, the nanotube strength and interfacial frictional stress are also estimated and range from 15-25 GPa and 40-200 MPa, respectively. These preliminary results demonstrate that nanotube-reinforced ceramics can exhibit the interfacial debonding/sliding and nanotube bridging necessary to induce nanoscale toughening, and suggest the feasibility of engineering residual stresses, nanotube structure, and composite geometry to obtain high-toughness nanocomposites.