It is well-known that wind power plants can provide short-term frequency control responses; however, when wind turbines are operated to extract maximum power from the wind, any additional energy supplied to the grid in response to the frequency event must be returned to the wind turbine to accelerate it back to optimum speed. The wind turbine must temporarily lower its power output to facilitate acceleration back to optimum speed. In power systems that have many wind turbines providing short-term frequency control services, the reduction in power generation associated with optimum speed recovery could be significant enough to cause a secondary frequency dip shortly after the initial dip, the nadir of which could be lower than the initial dip. This paper proposes 1) an improved speed-recovery scheme for wind turbines that provide synthetic inertia, and 2) a coordinated control scheme for wind turbines and BESSs to mitigate the secondary frequency dip that can occur during the synthetic inertia speed-recovery phase. The control schemes presented can be easily integrated into existing wind turbine and BESS active power controllers as implementation can be achieved using only the active power and rotational speed measurements that are available in the wind turbine's active power controller.