He also joined a team, which included medical specialists, at the scene of a coach crash exercise.
Iron Duke's captain, Cdr Mark Newland, said the exercise was a great opportunity to show the "broad range of skills a Royal Navy warship can bring to a disaster-ravaged island".
He said Sub Lt William Wales, as he is known onboard, was a natural leader and commanding small teams of people came as "second nature".
Prince William takes part in the exercise
He said: "Sub Lt Wales, as part of his remit on board, has been involved in the planning from the outset, and that's primarily in developing a plan and understanding of the nature of the infrastructure on Montserrat."
He went on: "With Sub Lt Wales, it's reasonably easy - what you have is an army officer who understands a military context.
"He understands instinctively the business of command and where his teams fit in there.
"What I have seen is his ability to integrate very quickly into teams, whether it be at the command level or the very low tactical level.
"Being sent away with a small group to lead and conduct a particular task - that, to him, is second nature."
William, who is an officer in the Household Cavalry regiment, is halfway through his stint onboard HMS Iron Duke, as part of a Royal Navy placement.
On 28 June the frigate, in a joint operation with the US Coast Guard, seized cocaine valued at £40m north east of Barbados in the West Indies.
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