Consolidating cubic boron nitride (cBN) typically requires either a matrix of metal bearing materials that are undesirable for certain applications, or very high pressures within the cBN phase stability field that are prohibitive to manufacturing size and cost. We present new methodology for consolidating high stiffness cBN composites within a hexagonal boron nitride (hBN) matrix (15-25 vol%) with the aid of a binder phase (0-6 vol%) at moderate pressures (0.5-1.0 GPa) and temperatures (900-1300 °C). The composites are demonstrated to be highly tailorable with a range of compositions and resulting physical/mechanical properties. Ultrasonic measurements indicate that in some cases these composites have elastic mechanical properties that exceed those of the highest strength steel alloys. Two methods were identified to prevent phase transformation of the metastable cBN phase into hBN during consolidation: 1. removal of hydrocarbons, and 2. increased cBN particle size. Lithium tetraborate worked better as a binder than boron oxide, aiding consolidation without enhancing cBN to hBN phase transformation kinetics. These powder mixtures consolidated within error of their full theoretical mass densities at 1 GPa, and had only slightly lower densities at 0.5 GPa. This shows potential for consolidation of these composites into larger parts, in a variety of shapes, at even lower pressures using more conventional manufacturing methods, such as hot-pressing.