A combined experimental and numerical investigation of the heat transfer characteristics inside an impingement cooled combustor liner heat shield has been conducted. Due to the complexity and irregularity of heat shield configurations, standard correlations for regular impingement fields are insufficient and detailed investigations of local heat transfer enhancement are required. The experiments were carried out in a perspex model of the heat shield using a transient liquid crystal method. Scaling of the model allowed to achieve jet Reynolds numbers of up to Rej=34,000 without compressibility effects. The local air temperature was measured at several positions within the model to account for an exact evaluation of the heat transfer coefficient. Analysis focused on the local heat transfer distribution along the heat shield target plate, side rims, and central bolt recess. The results were compared with values predicted by a standard correlation for a regular impingement array. The comparison exhibited large differences. While local values were up to three times larger than the reference value, the average heat transfer coefficient was approximately 25% lower. This emphasized that standard correlations are not suitable for the design of complex impingement cooling pattern. For thermal optimization the detailed knowledge of the local variation of the heat transfer coefficient is essential. From the present configuration, some concepts for possible optimization were derived. Complementary numerical simulations were carried out using the commercial computational fluid dynamics (CFD) code ANSYS CFX. The motivation was to evaluate whether CFD can be used as an engineering design tool in the optimization of the heat shield configuration. For this, a validation of the numerical results was required, which for the present configuration was achieved by determining the degree of accuracy to which the measured heat transfer rates could be computed. The predictions showed good agreement with the experimental results, both for the local Nusselt number distributions as well as for averaged values. Some overprediction occurred in the stagnation regions, however, the impact on overall heat transfer coefficients was low and average deviations between numerics and experiments were in the order of only 5–20%. The numerical investigation showed that contemporary CFD codes can be used as suitable means in the thermal design process.