It is important for modern scanning microwave microscopes to overcome the effect of the surface roughness. Here, we report microwave conductivity imaging of the phase-separated iron chalcogenide K$_x$Fe$_y$Se$_2$ ($x=0.8$, $y=1.6$-$2$), in which electric conductivity-induced contrast is distinguished from topography-induced contrast using a combination of a scanning tunneling microscope and a scanning microwave microscope (STM-SMM). We observed the characteristic modulation of the local electric property that originates from the mesoscopic phase separation of the metallic and semiconducting phases in two different scanning modes: constant current (CC) mode and constant $Q$ (CQ) mode. In particular, CQ scanning is useful because we obtain a qualitative image in which the topographic contrast is largely eliminated without degradation of the spatial resolution.
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