Offer a contingent payment of 10% (or similar) of the savings pr. month for one year after the migration. If a migration doesn't make sense then it won't happen

Offer a contingent payment of 10% (or similar) of the savings pr. month for one year after the migration. If a migration doesn't make sense then it won't happen and the client doesn't pay (would be very rare!) but when a migration happens 10% of the savings is probably more than you would have charged by the hour or quoted as a fixed price.