A quantitative microanalysis of astromaterials (e.g., meteorite, returned samples from asteroids) is a key technology to understand the history of our solar system formation. To fulfill this, we developed an energy-dispersive X-ray spectroscopy (EDS) using a transition-edge sensor (TES) microcalorimeterarray on a scanning transmission electron microscope (STEM) for material analysis. To reduce the systematic errors of a spectral analysis, we investigated and constructed the response function of the STEM-EDS system, which consists of detection efficiency and a two-dimensional response matrix. The latter represents the pulse-height redistribution functions of the incident photons of different energies. Using the constructed response function, we demonstrated the quantitative determination of SiO2 film and confirmed that the number-density ratio of oxygen to silicon (=2.29(-0.29)(+0.32)) is consistent with the expected value of 2 within the statistical errors. We further study the systematic errors of the concentration determination with simulations. We analyze the simulated spectra of TES-EDS and SDD (silicon drift detector)-EDS without a priori knowledge about the continuum spectra and find that the systematic deviations of parameters from the model values are smaller than 1% for TES-EDS and larger than 10% for SDD-EDS.