Speak with the staff as soon as you think you're going to miss your connecting train.

If it's a train with optional reservations, you can always use it and find a free seat (and get a refund for the reservation). If you have time at the station, you can request a free exchange of your reservation to the next train.

If your connecting train has mandatory reservations, then always speak with a member of staff to get an exchange (which must be free of charge) or to get your reservation endorsed for the next train.