I love the idea of suspending a taonga, special stone that has been beautifully shaped from your neck. Sometimes you can incorporate a hole into the design to hang it from, sometimes you need to drill one just for the purpose. I really prefer keeping the carving as intact as possible, for me it feels like this retains more integrity and mana/strength of the pounamu.
When I first learned how to carve and lash Hei Toki I drilled them all then covered that with the toki lashing. I pondered this for a long time until I worked out a way that would work to bind it with out drilling the stone. This makes the lashing functional, important, and an integral part of the taonga. Pounamu is best left without unnecessary holes.