Are there nonstop flights from Amsterdam (AMS) to Cartagena (CTG)?

Yes. KLM fly this route. Flight time is about 10h 25m.

What is the fastest connection from Amsterdam (AMS) to Cartagena (CTG)?

via Punta Cana ≈ 10h 55m, via Madrid ≈ 11h 49m, via New York ≈ 11h 50m (estimated flying time, excluding layovers).

from 35,000 ANA miles (economy, one way, based on the published award charts).

Amsterdam Airport Schiphol (AMS) to Rafael Nuñez International Airport (CTG)・8,431 km

Nonstop flights available (1 airline). Flight time about 10h 25m. Nonstop return flights also operate.

With milesANA 35,000 miles+ (via YUL)Economy, one way, estimate. Tap a connection for miles by cabin.

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.