I had a similar situation regarding my father as he past away at sea whilst working
as far as i can remember i had to contact the royal navy. In answer to your question.
"Do those lost at sea get certificates?" The answer is "YES THEY DO GET A DEATH CERTIFICATE"
You will need to contact the BMD Register in the area where the accident occoured and inform them that he past away at sea and they should be able to give you the address for the department of the Royal Navy where you will need to send the information and fee