I don't think specific ship renown has much to do with the award system. As this earlier reply in the U.S. Medals Fix thread
states, there doesn't seem to be a connection.
Tonnage, ship quality (decided by Type rather than renown), successful patrol quantity, I believe make up the qualifications for the system. AND, I believe the option for game Realism plays a role as well. The higher the Realism....the greater the modifier to the system.