Dubrovnik Airport is not in Montenegro but it is just 30 km away from Herceg Novi which is one of the most popular coastal cities in Montenegro. It is 48 km to Tivat and Dubrovnik airport to Kotor is 71 km. As it is located in Croatia it is advised to check visa requirements before you travel.
There is public transportation from Dubrovnik Airport to Dubrovnik and from Dubrovnik to some of the towns in Montenegro but it is not the cheapest and the easiest way to travel. The most convenient way to go to Montenegro from Dubrovnik Airport is by booking a private transfer before you travel.
There are flights from Istanbul, Geneva, London, Madrid, Edinburgh, Birmingham, Zagreb, Dublin, Brussels, Stockholm, Oslo, Copenhagen, Prague, Vienna, Paris, Barcelona, Cork, Munich, Rome, Frankfurt, Riga, Dusseldorf, Rotterdam, Athens and Amsterdam with Turkish Airlines, Austrian, Croatia Airlines, Easy Jet, SAS, Transavia, Eurowings, Lufthansa, British Airways, Air Baltic, United Airlines, TAP Portugal, Asiana Airlines, Air India, Iberia, Qatar Airways, Vueling, Aer Lingus, Polish Airlines, Air Canada, American Airlines, Norwegian Air, Trade Air, Brussels Airlines and Jet2.