A thorough numerical analysis of micro-impingement cooling for application in high pressure turbine vanes is presented. The fundamental flow of an axisymmetric jet is first modeled and studied to ascertain the validity of the results. Subsequent, a fully three dimensional curved vane is modeled with an in-line impinging array of jet diamters 0.5mm. The analysis reveals that spent air collects with increasing streamwise distance from the leading edge, thereby increasing jet exit velocities across the array. For all cases studied, an increase in jet to target spacing increased the overall Reynolds number of the array, but decreased the average heat transfer rate. Micro diameters of 0.25mm were subsequently studied for full vane geometry. For a given mass flow per unit of heated area, the micro-jets considerably increased the average heat transfer by 63%. Similar enhancements were obtained at a fixed pressure drop percentage, and for a desired average heat transfer.