Carbon geological storage (CGS) is an important global practice implemented to mitigate the effects of CO₂ emissions on temperature, climate, sea level, and biodiversity. The monitoring of CGS leakage and the impact of storage on hydrogeological properties is important for management and long-term planning. In this study, we show the value of passive monitoring methods based on measuring and modeling water-level responses to tides. We review how monitoring can be used to identify time-varying horizontal and vertical permeabilities as well as independently detect time-varying fracture distribution in aquifer–caprock systems. Methods based on water-level responses to Earth tides are minimally invasive, convenient, economic (since they use existing groundwater wells), and time-continuous. We show how measurements can be used to detect aquifer leakage (caprock confinement) and the distribution of surrounding faults and fractures, which are the two most important unsolved quantities in assessing geological CO₂ storage strategies.