Are there nonstop flights from Rome (FCO) to Podgorica (TGD)?

Yes. Wizz Air, Air Montenegro fly this route. Flight time is about 1h 11m.

What is the fastest connection from Rome (FCO) to Podgorica (TGD)?

via Belgrade ≈ 2h 12m, via Catania ≈ 2h 24m, via Budapest ≈ 2h 39m (estimated flying time, excluding layovers).

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

Rome–Fiumicino Leonardo da Vinci International Airport (FCO) to Podgorica Airport / Podgorica Golubovci Airbase (TGD)・581 km

Nonstop flights available (2 airlines). Flight time about 1h 11m. Nonstop return flights also operate.

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

7 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.