The back side recessed cooling surface of a shroud defining in part the hot gas path of a turbine is electrochemically machined to provide surface roughness elements and spaces therebetween to increase the heat transfer coefficient. To accomplish this, an electrode with insulating dielectric portions and non-insulating portions is disposed in opposition to the cooling surface. By passing an electrolyte between the cooling surface and electrode and applying an electrical current between the electrode and a shroud, roughness elements and spaces therebetween are formed in the cooling surface in opposition to the insulating and non-insulating portions of the electrode, hence increasing the surface area and heat transfer coefficient of the shroud.