Originally Posted by SK AAR

Why do you expect the Rome -BUD flight to be delayed? Most flights arrive as scheduled or with only a minor delay, so most likely you will make the second flight (provided that there is amble time to make the transfer of course). I wouldn't worry too much. If the first flight is delayed and you miss your second flight, it is likely that your travel insurance will cover the cost of purchasing new ticket; check the rules of your travel insurance.