Characterization of the elemental distribution of samples with rough surfaces has been strongly desired for the analysis of various natural and artificial materials. Particularly for pristine and rare analytes with micrometer sizes embedded on specimen surfaces, non-invasive and matrix effect-free analysis is required without surface polishing treatment. To satisfy these requirements, we proposed a new method employing the sequential combination of two imaging modalities, i.e., microenergy-dispersive X-ray fluorescence (micro-XRF) and Raman micro-spectroscopy. The applicability of the developed method is tested by the quantitative analysis of cation composition in micrometer-sized carbonate grains on the surfaces of intact particles sampled directly from the asteroid Ryugu. The first step of micro-XRF imaging enabled a quick search for the sparsely scattered and micrometer-sized carbonates by the codistributions of Ca2+ and Mn2+ on the Mg2+- and Fe2+-rich phyllosilicate matrix. The following step of Raman micro-spectroscopy probed the carbonate grains and analyzed their cation composition (Ca2+, Mg2+, and Fe2+ + Mn2+) in a matrix effect-free manner via the systematic Raman shifts of the lattice modes. The carbonates were basically assigned to ferroan dolomite bearing a considerable amount of Fe2+ + Mn2+ at around 10 atom %. These results are in good accordance with the assignments reported by scanning electron microscopy-energy-dispersive X-ray spectroscopy, where the thin-sectioned and surface-polished Ryugu particles were applicable. The proposed method requires neither sectioning nor surface polishing; hence, it can be applied to the remote sensing apparatus on spacecrafts and planetary rovers. Furthermore, the non-invasive and matrix effect-free characterization will provide a reliable analytical tool for quantitative analysis of the elemental distribution on the samples with surface roughness and chemical heterogeneity at a micrometer scale, such as art paintings, traditional crafts with decorated shapes, as well as sands and rocks with complex morphologies in nature.