Most emergency passport calls arrive in one of three shapes: the passport is at home and the traveler is at the airport; the passport is in a hotel safe two countries away; or a visa appointment, closing or funeral is tomorrow and the passport is with someone else. The first question in each case is the same, and it is not "how fast can you be here". It is "where exactly is the passport, and who can physically hand it over".
Once that is answered, the timing is usually straightforward. This page sets out what a courier can realistically do in the next few hours and days, and what you should do in parallel.
What happens in the first hour after you book
You enter the pickup and delivery locations and see a price, a pickup window and a delivery window. You book and your card is authorized, not charged. Our Operations Center, staffed around the clock every day of the year, looks at which of our couriers is closest to the pickup, which flights actually get the passport there in time, and whether anything about the route needs checking. In most cases you have a confirmation within 30 minutes and the payment is captured at that moment. We then let you know the courier's full name and the flight itinerary.
If the flights available at short notice cost more than your quote assumed, you are asked to approve the difference before anything is charged. If the best achievable arrival is more than four hours later than the window you saw, you are asked about that too. In both cases you can decline and pay nothing. If we cannot find a workable combination at all, we tell you, cancel the booking and release the authorization.
From then on the status updates follow the courier: en route to pickup, arrived, collected, at the airport, through security, boarded, departed, landed, en route to delivery, delivered. If a flight is cancelled or badly delayed, operations rebooks the courier and sends you a revised arrival time. We cannot prevent an airline from cancelling, but we do not leave the courier standing at the gate either.