Sarajevo remains one of the more delightfully obscure endpoints for a premium cabin traveler out of the Southeast, and there is no nonstop way around it: business class from Raleigh to Sarajevo requires a European connection, typically routed through Frankfurt or Munich on Lufthansa, or via Istanbul on Turkish Airlines. Delta passengers will generally piece together a codeshare through Amsterdam or Paris to link with a partner into Sarajevo, since Delta itself doesn't fly the European leg. My own preference after years working this corridor is the Lufthansa routing — RDU's Delta-operated transatlantic segment (often in an older Delta One suite, depending on aircraft assignment) connects smoothly to Lufthansa's short-haul business class into SJJ, and if you're fortunate enough to land a widebody with Lufthansa's newer Allegris cabin on the transatlantic portion itself, it's a noticeably elevated experience over the standard European regional product.
Turkish Airlines via Istanbul is worth serious consideration too, particularly for the layover itself: Istanbul Airport's Turkish Airlines Lounge is one of the more spectacular business lounges in the world, complete with a live cooking station and even a small cinema room, making a four-to-five-hour connection feel more like a destination stop than a chore. My insider tip: build in the longer Istanbul layover deliberately rather than chasing the tightest connection — the lounge alone justifies it, and Turkish's short regional hop down to Sarajevo is comfortable enough that you won't feel shortchanged after using the layover to rest and eat properly.
Seasonality matters enormously here — Sarajevo sees a summer tourism surge tied to its Ottoman old town and surrounding mountains, so fares and availability tighten considerably from June through August. January through March and October into November are your windows, both for award space and better business fares, as European carriers rebalance capacity during shoulder season. Given how few daily options exist on this route, setting up automated fare alerts is genuinely the smartest way to catch the occasional pricing anomaly before it disappears.