Montenegro’s ongoing investment with a €23million modernisation programme for its two international airports, Podgorica and Tivat, will make sure that future demand is catered for as the country becomes more popular.

In the summer accessibility from the UK is provided by a direct weekly flight from Heathrow to Tivat with JAT airlines (May – September).  Direct flight times from London are 2 ½ hours.  A daily service also operates from London to Belgrade and on to Tivat or Podgoric via a short transfer flight of 40 minutes. 
JAT (Yugoslav Airlines) flies from Belgrade to Tivat and Podgorica several times a day, so taking a flight with any airline to this more popular airport in Serbia should allow you the opportunity to travel on to Montenegro. 

Montenegro Airlines fly daily between Podgorica and Belgrade, and Podgorica to Budapest, Frankfurt and Zurich; while Lufthansa and Aeroflot also fly between Podgorica and Belgrade.

BA offer daily flights to Dubrovnik in Croatia, 20 minutes from Montenegro's border.  
JAT also operates inexpensive buses between the arrival airports and city centres.  

http://www.jat.com/ 

http://www.montenegro-airlines.cg.yu/eng/