My first job I was a wreck. I never let it show, but all that kept going through my mind was "I have absolutely no business doing this, what the hell was I thinking!".
The thing is, If you just dive in head first, do the best you can do...and then try as hard as you can to do even better, you'll push yourself into a place you've never been before. And as Pyrochan above me says, no one is looking at your art and thinking 'I hate this guys art, I'll ask him for a commission and just hope hecan paint like Rembrandt for me'.
Yeah, everyone gets that. When I first started doing jewelry commissions, I got over it by posting a picture of the finished piece before asking for payment. (With drawings, the piece has to be HEAVILY watermarked, or you won't get any money for it!) On especially complicated custom orders, I sometimes post concept sketches for approval first.
I've overwhelmingly found that no matter how self-critical I am, the client is almost always overly enthusiastic about how awesome it came out. I still post the finished piece before I ask for payment, but it's just for the client's sake now.
As you do more commissions, you'll feel more confident too.
The thing I keep thinking to myself is, that these people have asked me knowing what I can do, from my dA or from my folio. They wouldn't ask me if they didn't want the product I make at the standard I can currently make it.
I do get the same anxieties, I think we all do somewhere, but just take each commission one at a time and if in doubt reference.