I've often wondered what happened to pieces of jewellery too!

When Henry died, all of the 'queens jewels' would haver reverted back to the crown.  Catherine Parr had a hard time getting her own jewellery back from the Duke of Somerset, pieces that Henry had given to her over the course of their marriage and had given instructions that when he died, Catherine could keep.  It was a major bone of contention between the Duke of Somerset (the new Protector) and Catherine and her new husband, Thomas Seymour.  Sadly I don't think Catherine ever got her jewels back.  So I assume that particular piece would have stayed in the crowns' possession at least until the time of Elizabeth.  I don't think the necklace part was refashioned into another piece as there is a portrait of Elizabeth when she first became queen (I'd upload a picture but my laptop is throwing major hissy fits with these sort of things at the moment, sorry!) that shows her wearing a two-strand necklace that looks very similar to the Jane Seymour/Katherine Howard piece, sort of precious jewels set in gold Tudor roses with clumps of pearls in between. Unfortunately a different pendant is attached to it!

I don't know what happened to that particular pendant, most likely the jewels refashioned into other pieces and the gold melted down for use elsewhere.  It's not totally impossible that it was sold off to raise ready cash or given to foreign monarchs as a gift, though I don't know often those sort of things happened or if it was entirely legal.  So it's not completely beyond the realms of possibility that it could have ended up intact in the collection of the house of Bavaria!  

It's too bad that a lot of the crown jewels were sold off and melted down during the Civil War (after the portrait of Magdalena was painted though) – that's probably what happened to a lot of the Tudor-era jewellery.  But I did read somewhere that pearls once belonging to Mary Queen of Scots and purchased by Elizabeth after her execution are now part of the Imperial State Crown.