Wasserlinie ASDP Kewapante (Maumere)-Pulau Besar-Maropokot-Kewapante auf der Karte von Maumere

There is a regular ASDP ferry from Maumere to the islands in front and further down the northwest coast.
The ferry departs and arrives in the ferry harbour of Maumere, located in Kewapante.

The ferry doesn't appear on the ASDP website as it is locally run - information can be found in the port on online in the local newspapers.
Prices are unknown but as usual moderate. Ferry port on Pulau Besar is unknown but most likely in Koja Doi (the main settlement).

Payment was still cash in 2021, but there is a transition ongoing to cashless payment. The cashless payment is complicated: you need to pay online via transfer (indonesian bank only) or via (indonesian) flashcard (BNI, BRI, Mandiri, ...) The latter you can buy and top up in any Indomaret/Alfamart. An alternative option is to go buy the ticket in the nearest Indomaret/Alfamart and you can pay cash there (at a premium of course). With the payment slip you can enter the port where this paper will be changed to a ticket, with which you can board the ferry.