An experimental research study intended for the application of a planetary electrical discharge machining (EDM) process with copper-tungsten (Cu-W) electrodes in the surface micro-finishing of die helical thread cavities made with AISI H13 tool steel full-hardened at 53 HRC is presented. To establish the EDM parameters' effect on various surface finishing aspects and metallurgical transformations, three tool electrode Cu-W compositions are selected, and operating parameters such as the open-circuit voltage (U-0), the discharge voltage (u(e)), the peak discharge current (I-e), the pulse-on duration (t(i)), the duty factor (tau) and the dielectric flushing pressure (p(in)), are correlated. The researched machining characteristics are the material removal rate (MRR-V-w), the relative tool wear ratio (TWR-v), the workpiece surface roughness (SR-Ra), the average white layer thickness (WLT-e(wl)) and the heat-affected zone (HAZ-Z(ha)). An empirical relation between the surface roughness (SR-Ra) and the energy per discharge (W-e) has been determined. It is analysed that copper-tungsten electrodes with negative polarity are appropriate for planetary EDM die steel surface micro-finishing, allowing the attaining of good geometry accuracy and sharp details. For die steel precision EDM, the relative wear ratio optimum condition and minor surface roughness takes place at a gap voltage of 280 V, discharge current of 0.5-1.0 A, pulse-on duration of 0.8 mu s, duty factor of 50%, dielectric flushing pressure of 40 kPa and copper tungsten (Cu20W80) as the tool electrode material with negative polarity. The copper-tungsten electrode's low material removal rate and low tool-wear ratio allows the machining of EDM cavity surfaces with an accurate geometry and a "mirror-like" surface micro-finishing. A planetary EDM application to manufacture helical thread cavities in steel dies for polymer injection is presented. Conclusions are appointed for the planetary EDM of helical thread cavities with Cu-W electrodes validating the accomplishment as a novel technique for manufacturing processes.