Getting to Montenegro's Adriatic coast in genuine comfort requires threading together at least two connections, since no carrier offers anything close to nonstop service into Tivat's small coastal airport. There is no single-carrier business class from Jacksonville to Tivat, which means the real decision isn't which airline, but which European gateway you trust to handle the handoff smoothly. My preferred routing runs through Frankfurt or Munich on Lufthansa, connecting onward via Turkish Airlines through Istanbul or Croatia Airlines through Zagreb, since Tivat's limited runway and seasonal schedule (heavier May through September) demand flexibility on the last leg.
Lufthansa's long-haul segment out of the US is where you'll want to spend your comfort budget — their Allegris business class, now rolling out on select 787 and A350 routes, offers proper suites with closing doors on many aircraft, a meaningful upgrade over the older flat-bed product still flying some Atlantic routes. If your itinerary routes you through Istanbul instead, Turkish Airlines' business cabin is a worthwhile trade-off: their lounge in IST is genuinely one of the best in the alliance world, with a full brasserie, putting green, and cigar lounge that make a long layover feel like part of the trip rather than a delay. One insider tip that rarely gets mentioned: book the Zagreb–Tivat or Dubrovnik–Tivat connection with extra buffer time, as Croatia Airlines' regional jets operate on tight turnarounds and Adriatic coastal weather causes more schedule slippage than travelers expect.
Shoulder season — April, May, September, and October — consistently delivers the best combination of fare value and pleasant Montenegrin weather, avoiding both the summer yacht-season crowds in Kotor Bay and the premium pricing that comes with them. Because pricing on this three-carrier, multi-hub routing fluctuates more than on major transatlantic corridors, setting up fare alerts specifically for the Jacksonville–Tivat business class combination is the smartest way to catch the periodic dips before they disappear.