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Dynamically-tunable impedance matching is a key feature in numerous radio-frequency (RF) applications at high frequencies (10 s of MHz) and power levels (100s–1000 s of Watts and above). This work develops techniques that enable the design of high power tunable matching networks (TMN) that can be tuned orders of magnitude faster than with conventional tunable impedance matching techniques, while realizing the high power levels required for many industrial applications. This is achieved by leveraging an emerging technique – known as phase-switched impedance modulation (PSIM), which involves switching passive elements at the rf operating frequency – that has previously been demonstrated at rf frequencies at up to a few hundred Watts. In this paper, we develop design approaches that enable it to be practically used at up to many kilowatts of power at frequencies in the 10 s of MHz. A detailed analysis of the factors affecting the losses as well as the tradeoffs of a basic PSIM-based element is provided. Furthermore, it is shown how incorporating additional stages to the PSIM-based element, including impedance scaling and / or the addition of series or shunt passive elements, influences the losses and enables the efficient processing of high power levels given the limitations of available switches. A PSIM-based TMN that matches load impedances to 50 $\,\Omega$ and delivers up to 1.5 kW of power at frequencies centered around 13.56 MHz is implemented and tested over a load impedance range suitable for various industrial plasma processes.