An out-of-service Kyushu Shinkansen train carrying no passengers traveling on elevated bridges was derailed by the first event. This was the third derailment caused by an earthquake in the history of the Japanese Shinkansen, after one caused by the 2004 Mid-Niigata Prefecture Earthquake and another triggered by the 2011 Tohoku Earthquake. To analyze the mechanism of this third derailment, it is crucial to evaluate the strong ground motion at the derailment site with high accuracy. For this study, temporary earthquake observations were first carried out at a location near the bridge site; these observations were conducted because although the JMA Kumamoto Station site and the derailment site are closely located, the ground response characteristics at these sites differ. Next, empirical site amplification and phase effects were evaluated based on the obtained observation records. Finally, seismic waveforms during the first event at the bridge site of interest were estimated based on the site-effect substitution method. The resulting estimated acceleration and velocity waveforms for the derailment site include much larger amplitudes than the waveforms recorded at the JMA Kumamoto and MLIT Kumamoto station sites. The reliability of these estimates is confirmed by the finding that the same methods reproduce strong ground motions at the MLIT Kumamoto Station site accurately. These estimated ground motions will be useful for reasonable safety assessment of anti-derailment devices on elevated railway bridges.