This is an excerpt from the Jewellers and Watchmakers of NZ website, and is very good advice:

Jewellery Insurance

A Guide for Consumers

For your own protection and your responsibility to your insurance company

Check your insurance policy. Not only does the extent of the cover vary between insurance companies, so too do the procedures in the event of a claim.
Following a loss, insurance companies’ wordings may vary as follows:
In the event of a loss insurers may direct you to a nominated jeweller to have valuables repaired and or replaced or,
In the event of a loss insurers may allow you to nominate a jeweller at your discretion subject to a fair and reasonable quotation to replace, repair or reinstate.
Obtain an up-to-date appraisal of your jewellery and other valuable items every two to three years.
Keep an inventory of all your jewellery, specified or unspecified and where possible, receipts and details of when and where the item was purchased.
Have your jewellery inspected regularly by a JWNZ member to make certain that claws and mounts are in good condition.
The clasps and strings of cultured pearls and valuable beads should also be checked regularly.
Keep a separate inventory of all your jewellery at another location (other than your home), in case of fire, flood or peril.
Take care of all your jewellery. Gold and silver are precious metals and should be treated with due care as stress can result in damage. Keep your jewellery in a safe place at your residence.
It is advisable to photograph your valuable items or video your house contents to ensure that if a burglary does occur, you will be able to identify what is missing without relying on your memory.

Please note that most robberies centre on the master bedrooms – dressing tables and wardrobes.

Making an insurance claim

In the case of loss or theft of insured jewellery the Jewellers & Watchmakers of New Zealand Inc. would suggest the following procedure:

On discovery of loss, notify your local police station immediately. Obtain a crime report.
Immediately notify your insurance company or broker as to the nature and extent of your loss and request a claim form to be posted to you.
Complete the claim form in as much detail as possible. Your JWNZ member will offer you assistance and in most cases be prepared to act on your behalf.
In the event of you losing a gemstone take the claim form and article to your JWNZ jeweller for a quotation before returning it to your insurance company. Allow plenty of time to source a suitable replacement.

The information above was prepared as a consumer service by the Jewellers & Watchmakers of New Zealand Incorporated in conjunction with Mike Henry Insurance Brokers.