[en] A muonium atom is a system suitable for precision measurements for determination of muon's fundamental properties as well as for a test of quantum electrodynamics (QED). A microwave spectroscopy experiment of this exotic atom is being prepared at J-PARC, aiming at an improved relative precision at a level of 10"-"8 in determination of the muonic magnetic moment. A major improvement of statistical uncertainty is expected with the higher muon intensity of the pulsed beam at J-PARC, while further improvements depend on the size of systematic uncertainties. Reduction of various sources of systematic uncertainties are being studied: those arising from microwave power fluctuations, magnetic field inhomogeneity, muon stopping distribution and atomic collisional shift of resonance frequencies. Experimental scope and methods are presented in this paper, with an emphasis on our recent development of apparatuses and evaluation of systematic uncertainties. (author)