During transient events such as major solar eruptions, the plasma can be far from the equilibrium ionization state because of rapid heating or cooling. Nonequilibrium ionization (NEI) is important in rapidly evolving systems where the thermodynamical timescale is shorter than the ionization or recombination timescales. We investigate the effects of NEI on EUV and X-ray observations by the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamic Observatory and X-ray Telescope (XRT) on board Hinode. Our model assumes that the plasma is initially in ionization equilibrium at low temperature, and it is heated rapidly by a shock or magnetic reconnection. We tabulate the responses of the AIA and XRT passbands as functions of temperature and a characteristic timescale, n e t. We find that most of the ions reach equilibrium at n e t ≤ 1012 cm-3 s. Comparing ratios of the responses between different passbands allows us to determine whether a combination of plasmas at temperatures in ionization equilibrium can account for a given AIA and XRT observation. It also expresses how far the observed plasma is from equilibrium ionization. We apply the ratios to a supra-arcade plasma sheet on 2012 January 27. We find that the closer the plasma is to the arcade, the closer it is to a single-temperature plasma in ionization equilibrium. We also utilize the set of responses to estimate the temperature and density for shocked plasma associated with a coronal mass ejection on 2010 June 13. The temperature and density ranges we obtain are in reasonable agreement with previous works.