In this article, we summarize the theoretical matching boundaries and show the limitations they implicate for real-world amplifier design. Starting with a common schematic prototype, we investigate the question of how to realize its electrical response in a densely routed, massively parallelized layout. To that end, we develop a comprehensive study on the application of space-mapping techniques toward the design of high-power amplifiers (HPAs). We derive three reference design procedures and compare their performance in terms of convergence, speed, and practicality when laying out a densely routed HPA interstage matching network. Subsequently, we demonstrate the usefulness of the study by designing the networks of a compact three-stage eight-way wideband HPA in the Ka-band. The processed monolithic microwave integrated circuit features a 1-dB large-signal bandwidth of more than 11 GHz (a fractional bandwidth of 32.8%) and thus covers most of the Ka-band with an output power exceeding 6 W in 3 dB of gain compression. This demonstrates the highest combination of power and bandwidth to date using a reactively matched topology in the Ka-band.