If it's designer or valuable jewellery, I know places like Paris 99 in Melbourne purchase then re-sale high-end pieces. And a friend of mine, Lara McPherson is about to launch 'Wardrobe Wonderland' which I think may end up doing similar, or some version of re-selling/hiring pieces to people. Though both of these tend to deal in vintage and couture.

Otherwise, I would say the best place to sell second hand jewellery in Australia is Etsy. It has lots of designer stuff for re-sale, and because of the close-knit community on their site, I think counterfeiters and dodgy merchants are pretty quickly dealt with. The stores seem to have a more 'human' and legitimate reputation than those on eBay.

Cash converters, pawn shops? I can't imagine you would get much from them though.

Google consignment stores. They will offer your piece for sale then keep a cut of the sale price. 

We are Australian based and specialise in buying and selling diamond designer jewellery from luxury brands such as Tiffany & Co. Please check out our website here: www.catherinetrentonjewellery.com

Yes, we do.  We specialise in second-hand Tiffany & Co., Cartier and Bvlgari fine diamond Jewellery.  www.catherinetrentonjewellery.com

Not sure about your Tiffany & Co necklace but try to approach to the services that are buying diamonds, engagement rings or valuable stuff like that. I'm not sure they'll give you a great price, however, you can at least have a clue about the value of your item.

I think that the following website https://www.jaa.com.au/consumers/guidance/selling-your-jewellery will be helpful whether you are looking to sell jewellery in Sydney or anywhere else in Australia, or if you are looking to buy any. 

I haven’t heard of any such business in Australia, though it does sound like a good business idea!

Your options to sell second hand jewellery in Australia are:

1. Jewellery stores

Some jewellery stores will buy second hand jewellery, but they may not buy everything. It depends on their customer base, what type of jewellery they like and which designs appeal the most. So, if you’re selling a Tiffany & Co. necklace, approach jewellery stores in Sydney that sell preloved Tiffany & Co jeweller, too.

2. Consignment stores

The other quicker option is using consignment stores. There’s a few that’s online too such as Collector Square. People are open to buying jewellery online. Consignment stores will sell your preloved jewellery and valuables on your behalf, which means they take care of valuation, photos, finding buyers and selling. Of course, they will take a percentage of your sale proceeds.

3. Pawnshops

The last option is going to the pawnshop or Cash Converters. They won’t give you the best price so be prepared to take a big loss.  
 
If you’re looking for independent jewellery appraiser to value your necklace, you can try the National Council of Jewellery Valuers. They have a list of valuers on their site.

I too have a Tiffany & Co Necklace I'd like to get evaluated, only thing is it has been personalised (pendant) and has a diamond

If you want an easy option, look for consignment shops that sell jewellery, especially branded ones like Tiffany & Co. Generally, brand names like Bvlgari, Tiffany, Cartier, Chopard and Mikimoto for pearls, have a lot of demand as people are searching for them online. It should be fairly easy to sell them.