Omaha isn't a market where premium cabins to the Balkans get discussed often, which is precisely why savvy travelers should pay attention: there is no nonstop option, and business class from Omaha to Zagreb requires a routing through a major hub, typically Atlanta, Amsterdam, or Frankfurt via Delta and its joint-venture partners, with a total journey of roughly 11 hours of actual flight time plus connection. My preferred build is Delta out of OMA into Atlanta, then onto a Delta One transatlantic hop into Amsterdam or Paris, followed by a Croatia Airlines (OU) regional segment down into Zagreb — Croatia Airlines doesn't operate widebody business class, but its short intra-European business cabin is perfectly comfortable for the final leg. Alternatively, Lufthansa routings via Frankfurt or Munich put you into Lufthansa's business class product, and depending on aircraft assignment on the long-haul segment, you may find yourself in the newer Allegris business suite, though older 747-8 or A340 configurations are still common on U.S. routes, so don't assume the newest hardware.
The Frankfurt connection is my personal favorite for this itinerary: Lufthansa's FRA hub has strong short-connection infrastructure, and the Lufthansa Business Lounge in Terminal 1 is worth arriving early for, especially if you're facing a tight turn onto a Zagreb-bound regional jet. One insider tip that rarely gets mentioned — booking the Delta/Croatia Airlines combination through Amsterdam rather than Frankfurt often opens up better award availability in shoulder season, since KLM's Zagreb frequencies are less contested than Lufthansa Group's Munich-Zagreb routing, which fills quickly with connecting Balkan diaspora traffic.
Seasonality matters enormously here. January, February, March, October, and November consistently produce the softest fares and best award space, since Zagreb's tourist crush (and demand spike) runs May through September. Given how thin and volatile premium inventory is on this Omaha-to-Zagreb corridor, I'd strongly recommend setting up automated fare and award alerts rather than manually checking — the sweet spots open and close fast, often without warning.
