Interesting question. I've seen some ceremonial clothes of one of the Stuart kings at (I think) the Victoria and Albert museum, and I remember seeing some 18th century court dresses in a display at Kensington Palace. But I don't know if anything authentically belonging to Elizabeth I still exists anywhere. I know the crown jewels used by the Tudors and Stuarts were pretty much destroyed by Cromwell, and I wouldn't be surprised if other items known to belong to royalty were either destroyed or taken by Cromwell supporters.
Some of the pearls in the Imperial State Crown are said to have been from Elizabeth I's earrings, but I don't know if that's authenticated or just a rumour.
You could always send a question to Royal Insight magazine and see if they answer on the website; the "Ask a question" link is at the top right of this page:
http://www.royal.gov.uk/output/page1731.asp