Getting from the Sonoran Desert to the shores of the Adriatic is one of those routes that rewards patience and strategic routing, since no carrier offers a single-connection path that isn't a full day's journey. There is no nonstop business class from Tucson to Podgorica — and won't be for the foreseeable future — so the real decision is which hub personality you prefer for the long haul across the Atlantic. Delta routes you through Atlanta or JFK before handing off to a joint-venture partner in Europe, while Lufthansa's Frankfurt or Munich connections and Turkish Airlines' Istanbul gateway both offer a single European stop before the short hop down to Podgorica's compact Golubovci Airport. My preference after many attempts at this itinerary is Turkish via Istanbul: IST's business lounge is worth arriving early for, and Turkish's 787 and A330 business cabins offer proper lie-flat seating with reliable service consistency on the transatlantic leg from North America.
Lufthansa is worth considering if your Tucson positioning flight connects well through Munich, since their newer Allegris business suites are being phased onto select long-haul aircraft, though you'll want to confirm equipment before booking, as older configurations still fly many U.S. routes. Delta's Atlanta hub advantage is the sheer frequency of departures, which gives flexibility if Tucson's regional flight schedule runs late — a real risk given TUS's limited daily connections to major gateways. My insider tip: build in a minimum three-hour connection in Atlanta or Frankfurt during winter months, since Podgorica's onward flights are thin and a missed connection can mean an overnight stay with few reroute options.
January through March and October into November consistently offer the softest fares and the best award space on this corridor, as Montenegro's tourist season quiets considerably outside summer. Given the routing complexity and fare volatility across three alliances, setting up automated fare alerts is the smartest way to catch a business class fare drop on this Tucson–Podgorica corridor before it disappears.