After a disruption most people search the same way they searched when booking the trip: one origin, one destination, cheapest fare. That is the wrong tool for a rescue situation.
What you need now is the earliest confirmed seat, and you are much more likely to find it if you widen the search in three directions at once: airline, airport and routing.
Two different searches
If the airline caused the disruption, your first search is not for a ticket to buy, it is for an option to request. Airlines can move you onto partner carriers under interline agreements, and agents do this when a passenger names a specific flight.
If you are buying a new ticket yourself, then speed and flexibility matter more than price optimisation. A fare that is forty dollars cheaper but leaves eleven hours later is not a saving when you add a hotel night.
Step by step
Step 1: List every airport that works for you
Include secondary airports within a sensible train or bus ride of your destination. Getting to a city two hours away tonight often beats arriving at the perfect airport tomorrow afternoon. Check the ground connection first so you do not land somewhere with no transport left.
Step 2: Search by alliance and partner, not only by brand
Look at which airlines fly your route today, then check which of them your carrier can rebook you on. Naming the flight number to the agent turns a vague request into a simple yes or no, and it is much quicker for them to action.
Step 3: Consider split routings
Two shorter hops through a different hub can appear when the direct search shows nothing. Be careful with tight self connections and separate tickets, but as a same day rescue this often works, especially in Europe and the United States where hubs are dense.
Step 4: Confirm the seat before you release the old one
Never cancel or accept a refund until the replacement is ticketed. Check that the new booking shows a seat and a ticket number, not just a reservation, and re add your baggage, meals or assistance requests, since those do not always carry across.
