Synchronized motion between two self-running oil droplets floating on an aqueous phase is reported. We describe the results of our observation on the interference between a pair of centimeter-sized nitrobenzene droplets undergoing back-and-forth motion on a waterway. The two droplets exhibit a swinging type of synchronization when a thin glass capillary is placed at the midpoint of the waterway with a narrow rectangle shape. Furthermore, 2:1 synchronized oscillation of the periodicities of this back-and-forth motion is generated when the capillary is shifted away from the center of the waterway. We discuss the mechanism of the emergence of synchronized swinging motion for the pair of droplets based on a simple mathematical model with nonlinear coupled differential equations.