Hi again...
As I understand it..... 
...the microfiche were the original means of public access to BDM records in pre-internet NZ. They contain surname, christian name and, for the births and deaths, a reference number which denotes the district in which the event was registered. The reference number on the marriage fiche is one of a matched pair, the other belonging to the spouse.
I have a feeling the reference numbers are actually the folio (page) numbers from the original registers but I may be wrong.
The microfiche are still found at the larger public libraries.
When the internet appeared BDM NZ transferred the BDM records onto their website. Unfortunately not all microfiche records seem to have survived the transfer and, equally annoying, the registration district information is no longer mentioned. And to top it all off the website numbering system bears no relation to the microfiche numbering system.
On the plus side - the website mentions parents of the child (births), the name of the spouse (marriages) and the age at death or date of birth of the deceased (deaths). And NZ genealogy research is a lot easier for those not actually in NZ.
So swings and roundabouts.
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Because the reference number is from the microfiche, not the website, the best thing to do is just phone up BDM NZ. Have your credit card ready
0800 22 52 52 (New Zealand only)
+64 (4) 463 9362 (Outside New Zealand)
Mention that the reference number is from the microfiche and that there is no corresponding entry on the website.
Make sure you ask for a printout, costing NZ$20.40, not a certificate. A printout is a scan of the original register. A certificate is not only more expensive (NZ$26.50) but may contain human error as it's a transcript of the original register.
You can also ask for the printout to be emailed to you as opposed to posting it out. There's no great difference in time taken to receive it but, if needed, it's a lot easier to zoom in on an electronic document than a paper document....(although that's Twiggy's opinion. Personally, I quite like dusting off the old magnifying glass and acting all sleuth like

Regards
Beg