I had the same problem. Broke mine while drying the car. Buy the fairlady Z badge. Much cheaper from the US and just use the Z part of it. Simples
Make sure you buy the correct finish (satin) there are some chrome versions also
http://www.thenismoshop.com/Nissan-JDM-Fairlady-Z-Rear-Trunk-Emblem-84895-CD40A--Nissan-350Z-Z33_p_105.html