Optically pumped spintronic terahertz emitters (STEs) have, in less than a decade, strongly impacted terahertz (THz) source technology, by the combination of their Fourier‐limited ultrafast response, their phononless emission spectrum and their wavelength‐independent operation. However, the intrinsic strength of the inverse spin Hall effect governing these devices introduces a challenge: the optical‐to‐terahertz conversion efficiency is considerably lower than traditional sources. It is therefore primordial to maximize at least their electromagnetic efficiency independently of the spin dynamics at play. Using a rigorous time‐domain treatment of the electromagnetic generation and extraction processes, an optimized design is presented and experimentally confirmed. With respect to the strongest reported spintronic THz emitters it achieves a 250% enhancement of the emitted THz field and therefore an 8 dB increase of emitted power. This experimental achievement brings STE close to the symbolic barrier of mW levels. The design strategy is generically applicable to any kind of ultrafast spin‐to‐charge conversion (S2C) system. On a broader level, our work highlights how a rigorous handling of the purely electromagnetic aspects of THz spintronic devices can uncover overlooked aspects of their operation and lead to substantial improvements.