Clearly nothing is too good for them - or, I imagine, the saluki, traditional Arab hunting dogs, that have their own hospital nearby - which is perhaps not surprising when you learn that a good bird can sell for more than $250,000.
Sitting in the waiting room until a technician was free to show us around, I watched as the nervous owners fussed over their falcons, occasionally picking them up on their wrists to exercise their wings, making comforting noises, sometimes taking off a bird's hood so it could see its surroundings, holding plastic plates for them to relieve themselves into and constantly asking the receptionists how things were progressing in the surgery beyond.
One particularly fierce-looking Arab in a red turban arrived with a magnificent pure white female falcon - which, one of my neighbours whispered, "is the most-prized kind" - and handed over with it a wing feather so it could be replaced.
It was all so fascinating that I was almost disappointed when the time came for our tour and we were ushered into the hospital museum for a briefing on the role of falcons in Arab culture.
Falconry, our guide told us, went back some 2000 years to a time when falcons were "used to capture meat for the pantry. Even today almost every Arab family has at least one falcon. There are probably 50,000 of them in Saudi, Qatar and the UAE. But now they are used for sport and for beauty contests."
Actual hunting with falcons was pretty much banned in Arab countries, because the main prey species were endangered "so big hunting expeditions go to Pakistan especially, China, Russia and Central Asia where it is still allowed".
It is an indication of the importance placed upon falconry that saker falcon is the national bird of the Emirates, he said, and the birds are so prized that falcons have their own passports - in fact he showed us one - their own seats on passenger aircraft, usually in first class, "are treated as family members, like a daughter or son, and often have their own health insurance".
That was an appropriate moment for us to be led through to the surgery where 22 falcons were either sitting on perches, being examined by the staff - the hospital has a team of 65 - or in two cases under anaesthetic.
One of the falcons lying asleep was having a wing feather re-attached with the aid of glue. "If they lose a feather," our guide explained, "their flight is unbalanced. We keep a supply of spare feathers here in case the missing one cannot be recovered."
The other had its claws clipped and polished with a grinder - "in the wild," we were told, "they would be ground down as a result of gripping rough rocks" - then its beak trimmed, polished and oiled. Finally the technician opened the bird's beak and eyes and within moments it was wide awake and able to stand unaided on its shiny new talons.
After watching this remarkable spectacle we were offered the chance to handle the falcons ourselves. A young American woman standing beside me had a falcon popped on to her wrist. She looked terrified and held it as far away as possible.
Because of my name I've always considered these raptors to be part of the family, so I was too excited to feel nervous. Instead, I see from the photos that I just beamed with pleasure at the beautiful bird as it sat on my wrist.
Our guide seemed pleased about this and showed me how if I held the falcon above my head and twisted my hand to and fro, I could cause it to flap its wings to maintain balance. Wow.
After that, when they asked for a volunteer to feed one of the birds, my hand was up as ... quick as a striking peregrine.
For this I was told to put on a heavy leather gauntlet and "close your hand very tightly" round the plucked body of a plump quail. Then a big falcon was put on my wrist, had its hood removed and promptly dived its beak into the quail, tearing off a big chunk of meat.
Its strength was remarkable and I could easily see why they had told me to hold on "very tightly" because otherwise it would have pulled the quail free. Even so it took only a couple of minutes for the food to disappear into that vicious-looking beak.
All too soon I had to hand the falcon back but not before I had the chance to give it a friendly smile and say, "Hi cousin. Nice to meet you. Get in touch if you ever visit New Zealand."
Falcons being birds of few words, he didn't reply. But his eyes signalled a bond between us.
CHECKLIST
Getting there: Etihad Airways and Air New Zealand operate a codeshare partnership from Auckland, Wellington and Christchurch, via Australia, to Abu Dhabi. Transtasman flights are with Air NZ. Etihad operates 11 flights a week from Sydney and daily flights from Melbourne nonstop to Abu Dhabi. From its base in Abu Dhabi Etihad flies to 86 destinations around the world.
What to do: Visit the Abu Dhabi Falcon Hospital.
Further informantion: See visitabudhabi.ae.
Jim Eagles visited Abu Dhabi with help from Etihad Airways, Air NZ and Abu Dhabi Tourism Authority