In this experimental study, phase synchronization is studied in pairs of nonlinear oscillators coupled through a movable support. In particular, the dynamics of two discontinuous mass-spring-damper oscillators and the dynamics of the classical Huygens' pendulum clocks are considered. In both systems the individual oscillators are self-sustained. It is shown that in both cases, the oscillators exhibit in-phase and anti-phase synchronization. All experiments are executed on a new experimental setup consisting of two controllable mass-spring-damper oscillators coupled through an elastically supported rigid bar. The results suggest, that the synchronized motion observed by Christiaan Huygens around 1650 in a pair of pendulum clocks mounted on a flexible support, in many cases can also be observed when the pendulum clocks are replaced by other self-sustained nonlinear oscillators.