An embroidery process with high geometrical accuracy is presented for antennas with fine details. Previous embroidery processes employed thicker threads, leading to resolution not better than 1 mm. Therefore, fine details (e.g., sharp corners) could not be realized, and geometrical accuracy was low, viz. > 1 mm. To overcome these limitations, in this letter we: 1) employ much thinner E-fibers to enable the “printing” of sharp corners, and 2) increase embroidery density to boost surface conductivity. Two Liberator E-fibers were tested: 1) 40-strand ( diameter = 0.27 mm), and 2) 20-strand ( diameter = 0.22 mm). Embroidery density was optimized using double-layer stitching of 7 threads/mm. To validate our embroidery approach, we fabricated and tested a dipole antenna with intricate details operating at 2.4 GHz. This design could not be formerly “printed” on textiles. Both E-fiber (40/20-strand) prototypes exhibited excellent performance, comparable to that of copper antennas. The achieved geometrical accuracy was ~ 0.3 mm (viz. 3 times better).