High profile candidates are problematic at the best of times. They have broad and deep experiences, and can see through nonsense at 500 metres.
You cant bluff a high profile candidate because if you do you are not only endangering your current search. The wide ranging influence of these candidates puts your business at risk if you are third party search. It puts your company hiring brand at risk if you are an in-house Recruiter.
But what if no one else is available to interview them? It does occasionally happen that senior candidates arrive for interview and lowly Recruiters, often young enough be their son or daughter, have to interview them. If that lowly Recruiter is you, what would you need to do to ensure that your interactions with the candidates are sufficient to move them through to the next stage of the process?:

Lower Your Expectations - Dont even think about fully engaging the candidate and trying to make a deep assessment of their suitability for the position. This is not the time to try to box above your weight class. By way of illustration, I remember doing exactly this with a senior candidate from the chemical industry many years ago. It wasnt a pretty sight, and I was already over 30 years old at that stage. To get a sense of it, imagine being stared down by a fully grown bull, with no possibility for escape.
Understand the Candidate - One of the nice things about interviewing high profile candidates is that their information is normally readily available. You will find them on most of the major listings like the American or European Chambers of Commerce, and many of them will be featured at conferences and presentation. They are easily googled, and you should normally get more than 5 references to them that you can check for details.
In addition, we are all fortunate to be recruiting at a time when social software sites have taken off. You are likely to find your candidate on Linkedin, Viadeo or Xing, or on the many other niche sites that dot the online landscape. New players like Zoominfo seems to offer a lot here but they dont cover that many countries just yet.
Understand the Job - Like any good Boy Scout you should always be prepared for any candidate. In this it means doing your homework extremely well, in far greater detail than you normally would.
You have to know the job deeply, and this does not mean being able to recite the listed characteristics of the ideal candidate from the Job Description (JD). For a candidate like this you would probably want to dispense with his Resume as quickly as possible, and get into something a bit more meaty.
High profile candidates know exactly what they bring to the table so they are more interested in seeing how their experience and knowledge will be used. They will want to know about the person that they will be working under, about where the company sees the division or factory going, about what career would be in this for him/her etc. Lists just dont cut it here. Be prepared.
Pay Your Respects - High profile candidates should have a Handle-With-Care sign around their neck. You dont need to take a subservient attitude here but you do need to get past the small talk quickly. Tell them you appreciate that their time is valuable and then show them by getting to the point quickly.
Listen, dont talk - In-house and third party Recruiters are not normally known for a lack of confidence. They need to have the skill to engage candidates quickly, and they normally have something to offer, like a career or increased responsibility. Many are quite extroverted individuals who have the audicity to imagine they can engage someone (guilty) and establish their fit with any particular role (guilty).
But high profile candidates need exactly the opposite approach and may be painfully aware that the person interviewing them is much less experienced than them. So use this to your advantage. Take the approach that you can learn a lot from the candidate about a whole variety of issues, including how your company is seen, how your industry is progressing, how successful people think, and so on. Treat the interview like a chance to meet Bill Gates and ask yourself: What would you ask him if you got a chance to meet face to face? And how hard would you listen?
Focus on Your Strengths - If you are a corporate Recruiter or third party headhunter it is likely that you have some knowledge of behavioral interviewing or psychometrics. If you interview according to this knowledge you will be able to create a psychological barrier between you and the candidate, one that will protect you from your own inexperience.
So you are likely to be much more forceful and effective than if you try to interview according to the candidates industry knowledge. At best he will simply give you the answers you seem to expect, and at worst he will subtly disparage your inferior knowledge.
Practice, Practice, Practice - I know that you are going to say that you have some number of years experience interviewing people, but when it comes to a really high profile candidate you dont.
My problem with my chemical industry candidate might have been solved if I had just tested out the questions that I was going to ask. At the very least it would have allowed me to modify the questions. In the best case scenario I would have been forced to come up with much more nuanced ones.
Fake It - Many years ago I found myself in front of a man who was supposed to be my boss, coach and mentor. He wasnt. Instead, looking back, he was a middle-ranked manager who had suddenly found himself promoted out of his depth. He had compensated by being overweaning and dictatorial.
One of his little methods was to use a set of glasses that looked like pince-nez ie. glasses that perch on the end of your nose. He had probably picked them up at an old Victorian antique store. He would stare down them menacingly and the funny thing was that when combined with his position it was intimidating, even slightly threatening. So, before you interview this candidate change your demeanour by what ever means are at your disposal: dark suits, brylcreem, sensible shoes, conservative ties etc. It might actually help.
Relax - Finally, I would suggest that the fear you have of the candidate is balanced by the fact that you hold an ace in your hand. You are truly the gatekeeper for the position on offer. This will act as a shield that will tend to make the candidate want to overlook your inexperience.
But dont let that go to your head, unless you actually want a bloodbath.