How does a diagnostic procedure for adult autism go?

My personal view is that autistic people who reach adulthood, sometimes late adulthood, without a diagnosis have often perfected various methods of passing as neurotypical. As such, I think that observation is not really all that accurate a way of judging autistic status and that personal histories and traits described by the person being assessed are much more relevant. 

I think that my viewpoint is supported by the many stories that are regularly related on this forum, of people being denied a diagnosis for idiotic reasons, such as: makes eye contact, can string a coherent sentence together, makes appropriate gestures, is not a nuisance to [neurotypical] society, has a sense of humour etc. etc.

My private diagnosis is having a different procedure. No testing, but I had a long interview as a pre-diagnostic, for which i chose to submit some notes on various topics which she said we would cover. That could be as short as 2 hours or as long as 5 hours, possibly longer I don't know. She reckons I am autistic so has put me forward for the formal diagnosis, which will be a much shorter interview with a psychiatrist. The wait time was 3 weeks from contact and making an appointment to the pre-diagnostic, then a few weeks until the formal diagnosis but can be as short as a week, but he is on holiday at the moment.

With the NHS the wait times are years, which is one reason I went private for this. This is the link for where I am getting mine from if you are interested, several of us have used this service and I would recommend it:

https://www.shropshireautonomy.co.uk/autonomyplus/pre-diagnostic

Edit to add this was by video chat.

I had one psychiatrist and one Occupational Therapist. Would the latter have skewed more towards the tests and observations side? I feel like that together they worked to ensure that both aspects were covered, then came together to discuss their independent conclusions.

It varies enormously. The NHS procedures, in general, are the longest, employ the largest number of clinicians and rely the most on testing. Private assessments usually involve fewer clinicians, often just one. In my opinion there is also a decided difference between psychiatrist-led and clinical psychologist-led assessments, with the former more reliant on patient history and the latter more reliant on tests and observation.

Thank you, it already helped me a lot that I see who can I turn to, to know there are both tests and in-person sessions. Now there is information I can rely on when looking for possibilities in my own area 

I can only speak to my own private assessment (the GP put me on the NHS list but it turned out to be a four year waiting list in my area).

Mine consisted of three sessions and a written questionaire - the first sesion with a male assessor, the second with a female assessor. Both in person. The third was over the phone with the female assessor, and about a week after those first two - it  allowed me time ahead of the call to think of other areas I wanted to bring up, and she had questions mostly related to my early years etc.  About an hour and a half of conversation in each of the three.

So each session  had a slightly different remits. In a way what they do depends on a certain amount of sleight of hand - if you know to much going inn you might be too aware of that, instead of just going with the generalities (though to some extent, like any conversation, that's unavoidable anyway - you're just in the reflexive mode you'd go into in any somewhat formal and slightly stressy question and answer session) so maybe I shouldn't detail what unfolded in the second session in particular. Nothing so out of left field that it's worth worrying about, but still probably best to not list or flag up what they retrospectively revealed to have been looking for via those 'exercises'.