Growing scientific evidence suggests that risks due to failure of critical infrastructures (CIs) will increase worldwide, as the frequency and intensity of extreme weather events (EWEs) induced by climate change increases. Such risks are difficult to estimate due to the increasing complexity and interconnectedness of CIs and because information sharing regarding the vulnerabilities of the different CIs is limited. This paper proposes a methodology for risk analysis of systems of interdependent CIs to EWEs. The methodology is developed and carried out for the Port of Rotterdam area in the Netherlands, which is used as a case study. The case study includes multiple CIs that belong to different sectors and can be affected at the same time by an initiating EWE. The proposed methodology supports the assessment of common cause failures that cascade across CIs and sectors. It is based on a simple, user-friendly approach that can be used by CIs owners and operators. The implementation of the methodology has shown that the severity of cascading effects is strongly influenced by the recovery time of the different CIs due to the initiating EWE and that cascading effects that result from a disruption in a single CI develop differently from cascading effects that result from common cause failures. For most CIs, vulnerabilities from EWEs on the CI level will be higher than the cascading risks of common cause failures on the system of CIs; moreover, cascading risks for a CI will increase after its recovery from the event.