We explore allowable leakage for carbon capture and geological storage to be consistent with maximum global warming targets of 2.5 and 3°C by 2100. Given plausible fossil fuel use and carbon capture and storage scenarios, and based on modeling of time-dependent leakage of CO2, we employ a climate model to calculate the long-term temperature response of CO2 emissions. We assume that half of the stored CO2 is permanently trapped by fast mechanisms. If 40 % of global CO2 emissions are stored in the second half of this century, the temperature effect of escaped CO2 is too small to compromise a 2.5°C target. If 80 % of CO2 is captured, escaped CO2 must peak 300 years or later for consistency with this climate target. Due to much more CO2 stored for the 3 than the 2.5°C target, quality of storage becomes more important. Thus for the 3°C target escaped CO2 must peak 400 years or later in the 40 % scenario, and 3000 years or later in the 80 % scenario. Consequently CO2 escaped from geological storage can compromise the less stringent 3°C target in the long-run if most of global CO2 emissions have been stored. If less CO2 is stored only a very high escape scenario can compromise the more stringent 2.5°C target. For the two remaining combinations of storage scenarios and climate targets, leakage must be high to compromise these climate targets.