Pulsed electrostatic gating combined with capacitive charge sensing is used to perform excited state spectroscopy of an electrically isolated double-quantum-dot system. The tunneling rate of a single charge moving between the two dots is affected by the alignment of quantized energy levels; measured tunneling probabilities thereby reveal spectral features. Two pulse sequences are investigated, one of which, termed latched detection, allows measurement of a single tunneling event without repetition. Both provide excited-state spectroscopy without electrical contact to the double-dot system.