Scotland's capital doesn't get a nonstop from the Twin Cities, which is precisely why savvy travelers plan their connection as carefully as their seat selection. There is no direct service on this route, so business class from Minneapolis to Edinburgh routes through either Amsterdam or London, with Delta operating the transatlantic backbone via its joint venture partnership with Air France-KLM, while British Airways and Virgin Atlantic funnel passengers through Heathrow before a short onward hop north. The most efficient itinerary I've found repeatedly is Delta's MSP–AMS segment in Delta One, followed by a KLM or Delta regional connection into EDI, keeping total journey time near the 8.5-hour mark once you account for the short hop.
Delta One's suite, now standard on many of its transatlantic widebodies, delivers a sliding door and genuine privacy that makes the Amsterdam connection painless, especially with a long layover to shower at the Air France-KLM lounge before continuing north. If you route via London instead, British Airways' Club Suite—with its own door and forward-facing bed—is the more comfortable choice over their older Club World cabins still flying some Heathrow routes, and Virgin Atlantic's Upper Class Suite on the A350 offers a genuinely excellent alternative with its herringbone layout and Clubhouse access at Heathrow's Terminal 3. My insider tip: book the Amsterdam routing whenever possible in shoulder season, since Schiphol's transfer security is far faster than Heathrow's, saving nearly 40 minutes that matters when connections run tight.
January through March and again in October and November are when fares soften meaningfully, as leisure demand for Edinburgh dips before festival season and after summer crowds clear out—exactly when business travelers should be watching hardest. Given how these three-carrier options fluctuate week to week depending on which hub has excess premium inventory, setting up fare alerts for this specific city pair is the smartest way to catch a Delta One or Club Suite award or paid fare before it disappears.