I asked in March before putting in my order, and the NSX was not yet in my insurance guy's system. It quoted the rate for a custom car with a stated value, and that quote was $4200/year. I didn't give much credence to that. I would guess I'll pay around $2000/year. I also have a C7 Z06 and am paying $1200/year. MSRP of NSX is about 2X, so I assume it will be a bit less than 2X for insurance.
I only had my GT-R for a year (beginning when they first came out-- 2008?) and honestly don't remember what I was paying for insurance on it.