Micro-Electro Discharge Machining (μ-EDM) is one of the nonconventional micro-machining processes in which electrical discharges are produced between the micro-sized electrodes - tool and workpiece immersed in dielectric fluid. The electrical discharges thus produced remove the workpiece material through melting and vaporization process and results in the creation of micro-craters. This paper focuses on machining of micro-channels on copper alloy - phosphor bronze plate using μ-EDM. Various micro-channels have been machined on phosphor bronze with input parameters: voltage, capacitance and pulse on-time varied at four levels. The experimental layout plans were designed with robust design technique - Taguchi-based L16 orthogonal array and the process parameters were optimized using optimization technique - Grey Relational Analysis (GRA). The dimensional aspects - depth, width, profile and surface roughness of machined channels were selected as output responses. The experimental results show that the parameters have individual and combined effect on responses. Analysis of Variance (ANOVA) technique has been used to explore the effect of parameters on responses. Detailed surface morphology of the machined features has also been analyzed using scanning electron microscope (SEM) and noncontact optical profiler images. As an extension of machining channels, Y-shaped channel has been machined on copper alloy which can be used for micro-fluidic applications. © 2020 World Scientific Publishing Company.