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We report on a systematic characterization of microbulk Micromegas readouts in high-pressure Ar+1%iC4H10 and Ne+2%iC4H10 mixtures. Experimental data on gain, electron transmission and energy resolution are presented for a wide range of drift and amplification voltages and pressures from 1 bar to 10 bar for argon and from 5 bar to 10 bar in neon, in steps of 1 bar. Maximum gains higher than 1.7e3 (1.7e4) in argon (neon) are measured for all pressures, remarkably without the significant decrease with pressure typically observed in other amplification structures. A competitive energy resolution at 22.1 keV, but with a slight degradation with pressure, is observed:from 10.8% at 1 bar to 15.6% FWHM at 10 bar in argon and from 8.3% at 5 bar to 15.0% FWHM at1 10 bar in neon. The experimental setup, procedure and the results will be presented and discussed in detail. The work is motivated by the TREX-DM experiment, that is operating in the Laboratorio Subterráneo de Canfranc with the mentioned mixtures, although the results may be of interest for other applications of time projection chambers at high pressures.