A picosecond laser system emitting laser radiation with 515 nm at 7 ps pulse duration was used in combination with a galvanometric scanner to produce optically transparent antennas. The antenna substrate material was 200 μm thick fused silica glass which was radio frequency (RF) sputtered with a 1 μm thick Cu coating. The antenna structure was generated by laser ablation of the Cu coating. The goal of the investigation was to find laser parameters which remove the Cu coating at maximum optical transparency of the ablated area and to identify the relationship between laser parameters, designed antenna layout and generated antenna geometry. The findings suggest that the patterning process should be realized at low fluencies in the range of Cu’s ablation threshold in combination with multiple irradiation cycles in order to remove the Cu coating without affecting the glass surface. Increasing the fluence or irradiation cycles increased the ablated area which decreased the width of the generated antenna traces. At the optimized laser parameters, a linear relationship between the designed layout trace width and generated trace width was found. The relationship enabled the production of antenna geometries with high precision which operated at the designed frequency.