I'm kind of sort of considering maybe thinking about picking up an early BMW Z3, mainly because they seem to be less rusty than the local Miatas. I've owned two Miatas. As soon as I put a cage in one, I couldn't stand driving the other because of the cowl shake. Are BMW Z3s less prone to cowl shake than Miatas?
Sounds like you need some butterfly bracing and frog arms on your street Miata (assuming its a NA).
Otherwise, I think all convertibles (made of metal) will have some cowl shake, especially as they age. I suspect the supercars made from CF/Kevlar, etc won't have quite that problem, but that's neither here nor there.
Get an S2000. No cowl shake heree. 
Sine_Qua_Non wrote: Get an S2000. No cowl shake heree.
Yup.
Z3's are pretty sturdy. They feel very much like a grown-up Miata. Even the 4cyl versions have decent power, and they are much more luxurious and comfortable than an NA or NB Miata.
I drove a very nice example around for a few weeks and never noticed cowl shake. Of course I also owned (and loved) a TR-6 and the shaking never bothered me. So YMMV.
The Z3 chassis has moderate cowl shake and is particularly noticeable when driving over train tracks or speed bumps. A front strut tower brace makes a huge difference on these cars and I have the following installed on my M (Z3) Roadster.
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