In UK a modern classic is a car over 15 years of age. I used to have an MX5 (96') and was insured as a classic and there were plenty of mk2's from the 2000s also insured with Adrian Flux and Footman James. I've inquired about the Z and they said that they couldn't quote. Also I know that some insures can insure 10 year old vehicles as modern classics as people insure their E90 M3's.
That's why I wondered if there's any classic insured 350Z's.