Copper matrix composites with zirconium diboride (ZrB2) were synthesised by ball milling and consolidated by Spark Plasma Sintering (SPS). Characterisations of the ball-milled composite powders were performed by scanning electron microscopy (SEM), X-ray diffraction, and measurement of the particle size distribution. The effect of the sintering temperature (1123 K, 1173 K, and 1223 K) and pressure (20 MPa and 35 MPa) on the density, porosity, and Young’s modulus was investigated. The relationship between the change of Orb content and physical, mechanical, and electrical properties was studied. Experimental data showed that the properties of Cu–Orb composites depended significantly on the SPS sintering conditions. The optimal sintering temperature was 1223 K with a pressure of 35 MPa. Composites exhibited a high degree of consolidation. For these materials, the apparent density was in the range of 93–97%. The results showed that the higher content of Orb in the copper matrix was responsible for the improvement in Young’s modulus and hardness with the reduction of the conductivity of sintered composites. The results showed that Young’s modulus and the hardness of the Cu 20% Orb composites were the highest, and were 165 GPa and 174 HV0.3, respectively. These composites had the lowest relative electrical conductivity of 17%.