Airlines PNG connects Alotau twice-weekly with the Trobriand Islands and with Misima in the Louisiade Archipelago.
Occasional cargo vessels connect the islands and it may be possible to get a ride on the deck. But, realistically, the best way to see Milne Bay is by sailing. The province attracts many yachties, particularly from Australia. The Louisiade Archipelago area is well charted but yachts tend to avoid the area around the Trobriands as charts are unreliable.