The Z has two rev limiters in fact. If you're in neutral and you slam the gas, the revs will stop at 5000rpm. It's a soft limiter. If you put the transmission in gear, regardless of being stopped and having the clutch depressed or if you're accelerating, then the limiter is set at 7500rpm. If you hit that, the engine will not rev higher. That's limiters and it shouldn't worry you - if the engine oil is hot enough (i.e. 90° Celsius) then it's perfectly fine to rev it - but don't abuse it.
Someone earlier mentioned downshifting instead of upshifting. Regardless of rev limiters, if you downshift instead of upshift, your wheels are turning at the same speed, while through the transmission, you will bring those revs to the engine, and if you downshift, you will bring revs up, regardless of what the engine rev limiter is. It will most likely break the engine, as it's not design to rev so high. More in this video, if you're interested:
https://www.youtube.com/watch?v=p9SbDvMhCFs
And then thirdly, the Z also has a shift light. There is a red colored light - yellow on newer models - which will start blinking when you're 500 revs below the set limit. This limit is NOT the rev limiter, but a limit that is factory set at 7000, which you can set yourself to any RPMs you'd like. So if you have a gf who drives your car and you want to limit her from driving like a maniac, you can set the shift light to 4000rpm and tell her the car will start blinking when she "must" shift and there you go. This will not affect the actual rev limiter, which is factory set at 7500. The shift light's function is to help you shift, seeing the blinking with peripheral vision, without actually strictly looking at the gauges.