What to do
Go straight to the airline transfer desk or the service counter and explain the situation with the boarding passes in hand. Ask what they can rebook you on today or early tomorrow. At the same time check train and bus options from the current airport city to your final destination or to a nearby city that still has late connections. Decide whether same-day arrival is critical or if an overnight stop is acceptable.

Three options
First option is a same-day rebooking on a later flight with the same airline or a partner. This keeps air travel and usually gets you there in the evening or late night. Extra travel time beyond the original plan is often two to six hours. Cost is frequently zero if the miss was caused by the first flight delay, otherwise a change fee plus possible fare difference can appear.

Second option is a direct train from the city of the missed connection to the final city. Many routes have afternoon or evening departures that take four to eight hours. You leave the airport by local transport, board the train, and arrive the same day or late evening. Ticket prices at short notice usually fall between 45 and 130 euros or dollars depending on distance and seat availability.

Third option is a long-distance bus or a mix of bus and regional train. This is slower, often six to eleven hours, but seats are more likely to remain and the price stays lower, commonly 30 to 85 euros or dollars. Overnight services exist on some corridors and can save a hotel night.

Cost
Airline rebooking after a missed connection is often free when the first flight was late, but not always. Trains and buses come from your pocket first. Keep every receipt and the original boarding passes. Some of those extra costs can be claimed later if the miss was within the airline’s control. Factor in local transport between airport and station, it adds a small but real amount.

Damage-control advice
Tell the airline counter you need the bags prioritised if they have not arrived yet. Photograph the departure board that shows the missed flight and keep the message or announcement if one was given. Write a short note of the times everything happened while they are still fresh. If you buy a train or bus ticket, choose one that still leaves a little buffer in case of further small delays. Message anyone waiting at the destination with the new realistic arrival window before you leave the airport.

Summary
A missed connection feels sudden but the same three paths keep appearing: later flight, train, or bus. Check the airline rebooking first, then look at surface options in parallel, pick the one that limits the damage to the rest of the day, and save every piece of paper. Most people who move through these steps within the first hour still reach the destination without losing the entire trip.