A major problem in software engineering is assuring the correctness of a distributed system. A certifying distributed algorithm (CDA) computes for its input-output pair (i, o) an additional witness w – a formal argument for the correctness of (i, o). Each CDA features a witness predicate such that if the witness predicate holds for a triple (i, o, w), the input-output pair (i, o) is correct. An accompanying checker algorithm decides the witness predicate. Consequently, a user of a CDA does not have to trust the CDA but its checker algorithm. Usually, a checker is simpler and its verification is feasible. To sum up, the idea of a CDA is to adapt the underlying algorithm of a program at design-time such that it verifies its own output at runtime. While certifying sequential algorithms are well-established, there are open questions on how to apply certification to distributed algorithms. In this paper, we discuss distributed checking of a distributed witness; one challenge is that all parts of a distributed witness have to be consistent with each other. Furthermore, we present a method for formal instance verification (i.e. obtaining a machine-checked proof that a particular input-output pair is correct), and implement the method in a framework for the theorem prover Coq.