Microchannel heat exchangers are used to remove the high heat fluxes generated in compact electronic devices. The roughness of the microchannels has a significant effect on the heat transfer characteristics, especially the nucleate boiling and pumping power. Therefore, development of predictive models of surface texture is of significant importance in controlling heat transfer characteristics of these devices. In this study, micro-Wire electrical discharge machining (mu-WEDM) was employed to fabricate metal-based microchannel heat sinks with different surface textures. First, experiments were conducted to achieve the desired surface roughness values. Oxygen-free copper is a common material in the cooling systems of electronic devices because of its high thermal conductivity and low cost. Design of experiment approach based on the Taguchi technique was used to find the optimum set of process parameters. An analysis of variance is also performed to determine the significance of process parameters on the surface texture. An artificial neural network model is utilized to assess the variation of the surface roughness with process parameters. The predictions are in very good agreement with results yielding a coefficient of determination of 99.5 %. The results enable to determine mu-WEDM parameters which can result in the desired surface roughness, to have a well-controlled flow and heat transfer characteristics for the microchannels.