Climate change poses a key challenge for biodiversity conservation. Conservation agencies, in particular, have to decide where to carry out conservation measures in a landscape to enable species to move with climate change. Moreover, they can choose two main governance modes: (1) buy land to implement conservation measures themselves on that land, or (2) compensate landowners for voluntarily carrying out conservation measures on their land. We develop a dynamic, conceptual ecological-economic model to investigate the influence of changes in climatic parameters on the cost-effectiveness of these governance modes and specific patch selection strategies (price prioritisation, species abundance prioritisation, climate suitability prioritisation, climate change direction prioritisation). We identify five effects that explain the cost-effectiveness performance of the combinations of governance mode and patch selection strategy and find that their cost-effectiveness depends on climate parameters and is thus case-specific.