Boat:
KRILO STAR from port of Dubrovnik and Split.
Tickets from the ticket office or online!
            
http://www.krilo.hr/en/

TP LINE from port Of Dubrovnik to Mljet (Sobra or Polače. Polače is closer to Pomena)
 
https://tp-line.aktiva-info.hr/eng/frmPregledSlobodnoEng.aspx


 Car Ferry:
Ferry stop (Prapratno) is 1 hour drive from Dubrovnik! 

Prapratno-Sobra
http://www.croatiaferries.com/prapratno-sobra-ferry.htm

Sobra-Prapratno
http://www.croatiaferries.com/sobra-prapratno-ferry.htm