Time‐dependent complex eigenfrequencies for traveling inertial waves in a rotating cylinder of fluid have been measured while the fluid was spun up from rest. The waves were excited by precessing the lid of the cylindrical container at a frequency near a predicted eigenfrequency for a given rotation speed. Time sequences of disturbance pressure differences measured during subsequent free ringdown of the excited wave were inverted to recover inertial eigenfrequency and decay rate using a generalized least‐squares procedure.