Are there nonstop flights from London (LGW) to Sarajevo (SJJ)?

No. The fastest connection is via Stuttgart, about 2h 53m of total flying time.

What is the fastest connection from London (LGW) to Sarajevo (SJJ)?

via Stuttgart ≈ 2h 53m, via Zurich ≈ 2h 54m, via Frankfurt am Main ≈ 2h 55m (estimated flying time, excluding layovers).

from 15,000 ANA miles (economy, one way, based on the published award charts).

London Gatwick Airport (LGW) to Sarajevo International Airport (SJJ)・1,606 km

No nonstop flights. The fastest connection is via Stuttgart (STR), about 2h 53m of flying time (layover not included).

With milesANA 15,000 miles+ (via ZRH)Economy, one way, estimate. Tap a connection for miles by cabin.

None.

15 one-stop options, sorted by estimated flying time. Tap one to see the airlines on each leg and booking links.

Times are estimated from distance. Check schedules, frequency and availability with the airline or a booking site.