The institutions of the Dutch (urban) planning system face four challenging characteristics of climate adaptation measures. These measures are uncertain in their effects, in competition with other interests, multifaceted, and inherently complex. Capacity building is a key issue for the implementation of climate adaptation measures in urban planning processes, which aim to achieve Climate-Proof Cities (CPC). For successful capacity building, it is important to define the relevant stakeholders and tailor the adaptation strategies first to (the position of) these stakeholders and next to the specific urban conditions and issues. In addition, scientific insights and tools can be of assistance, and the use of climate maps can help to create a common language. Such common understanding of climate problems can lead to "goal entwinement" between actors, which can support the implementation of climate adaptation strategies in urban planning. Awareness, recognition and urgency are the most important components of this common understanding, which may differ for each stage in every urban planning process. In order to overcome the pragmatism that rules in day-to-day urban planning processes, multi-level arrangements between different tiers of government must be employed to improve the penetration of climate adaptation measures. After all, it still remains a soft interest in a hard process.