VAT in Denmark

VAT refund forms need to get stamped when the goods leave the EU (same answer for any EU country, not just Denmark).

As you are buying "jewelry in Copenhagen and . . . . traveling to Stockholm by train and then leaving by plane.", that means Stockholm airport, unless you are flying to another EU country, in which case you get the forms stamped when you leave that country.

You need to get the VAT forms from the shop(s) when you make your purchases, and return the stamped forms to get your refund from the shop (not from customs).

What will I be looking for in the Stockholm airport?

After you have checked in, and gone through security, you need to find the customs office. They will stamp your forms to certify the goods have left the EU, intact and unused. They may want to see the goods, so it is sensible to have them in your hand luggage. Since they are valuable, it is probably a good idea to keep them with you.

You then return the completed forms to the shop (or their agent). When the shop has proof the goods have been exported from the EU (the stamped forms), they no longer have to pay the government VAT. So the shop (not the government) can refund the VAT that they charged you.

The airport website probably has some info on where the customs office is.

And make sure the jewelry is in its original case or however you acquire it. For example, you would not be permitted to wear it while in Europe, as it would then be a good that you consumed.

VAT is 20% of what you pay. My understanding is that the agent can stamp Global Blue forms from Denmark (choose them if there is choice in Denmark). Landside office: https://www.globalblue.com/tax-free-shopping/sweden/stockholm-arlanda-terminal-5
Expensive items must be validated at the airside office.