Madeira's volcanic runway has humbled many a pilot, and reaching that dramatic clifftop approach in a lie-flat seat rather than a cramped economy row makes all the difference after a long transatlantic haul. There's no nonstop option here—business class from Raleigh to Funchal always routes through a major European or UK hub, since RDU simply doesn't have the transatlantic density to support direct island service. In practice, that means booking through London on British Airways, Frankfurt or Munich on Lufthansa, or Lisbon on TAP Portugal, with TAP's connection being the most logical given Portugal's ownership of Madeira and the airline's frequent FNC rotations from Lisbon.
Of the three, I'd steer discerning travelers toward TAP if schedule allows, not because the hard product rivals its rivals—TAP's business class is comfortable but not groundbreaking—but because the Lisbon connection is short, familiar, and avoids the fatigue of a double long-haul-to-short-haul grind. British Airways routes through Heathrow, where Club Suite (their door-equipped, all-aisle-access seat rolled out across the 777 and A350 fleet) offers genuine privacy for the transatlantic leg from RDU, though you'll then downgrade to a short-haul business cabin for the Heathrow-Funchal hop. Lufthansa's Frankfurt or Munich connections work well too, particularly if your RDU-departure aligns with their evening transatlantic banks, and their long-haul business seats offer solid recline and Star Alliance lounge access during the layover. My insider tip: build in at least a two-hour connection window regardless of hub, since Funchal-bound flights often depart from remote stands requiring bus transfers, and missing that tight island rotation can mean a full day's delay given limited frequencies.
Deal-hunters should target January through March or October and November, when transatlantic business fares soften considerably outside peak summer and holiday demand. Given how thin scheduling is on this route, I'd strongly recommend setting up fare alerts rather than manually checking—award space and discounted business fares on these RDU-to-Funchal itineraries can appear briefly and vanish just as fast.