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Any system, company or complex task is composed by processes, i.e., sequences of actions performed in some established order. Some of these processes are considered sensitive for the role they play within the system, or for the sensitive data they manage. In such cases, the trust in this processes is desirable, requiring their verification, monitoring, auditing, but also the possibility of being insured by a third party. In this approach we propose a schema for insuring sensitive process based on the use of formal models and Process Mining techniques (i.e. process management techniques that allows for the analysis of processes based on event logs). The experimental results presented show that this new approach could be useful in the context of insurance and analysis of processes.