The dynamic characteristics of converter-dominated systems are governed by controlling power converters and the interactions between converter systems and conventional alternators. Frequency oscillations can appear under dynamic operation conditions caused by the phase-locked loop dynamics and interactions among the converter control systems. The oscillations may be poorly damped, which can result in reduced power generation, longer settling time, or disconnections of sensitive components. It is foreseeable that damping services will be critical for power grid stabilization in the future with high penetration of renewable generation. In this work, synchronous condensers (SCs) are evaluated and applied to provide damping services to the power grid under post-event conditions. An innovative supplementary controller for the automatic voltage regulator of SCs is proposed to improve the frequency stabilization in a converter-dominated system after disturbances. Using local and remote measurements, SCs are able to modulate the reactive power output and hence, the terminal bus voltage, which further impacts the power flow in the system; therefore, damping can be provided to the frequency oscillations. The control is implemented on an industrial-level hardware platform, and the performance is verified by the hardware-in-the-loop simulation.