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This paper proposes a multi-stage scale estimation algorithm using phase-based correspondence matching for electron microscope images. Consider a sequence of microscope images of the same target object, where the image magnification is gradually increased so that the final image has a very large scale factor S (e.g., S=1,000) with respect to the initial image. The problem considered in this paper is to estimate the overall scale factor S of the given image sequence. The proposed scale estimation technique provides a new methodology for high-accuracy magnification calibration of electron microscopes. Experimental evaluation using Mandelbrot images as precisely scale-controlled image sequence shows that the proposed method can estimate the scale factor S=1,000 with approximately 0.1%-scale error. This paper also describes an application of the proposed algorithm to the magnification calibration of an actual STEM (Scanning Transmission Electron Microscope).