This thread gives me an opportunity to remind us that this brooch was not the first jewel which is presented to a member of the British Royal Family by the Czech Republic.
In 1996, during her State visit to the Czech Republic, Queen Elizabeth II received as gift from the Municipality of Brno (the second largest city of the country) a very nice garnet and gold parure, comprising a necklace, a bracelet, a brooch and a pair of earrings. This gift was very appropriate, as the Czech Republic is the main productor of garnets.
Unfortunately, the Queen has never worn this parure publicly (as far as I know - if I am wrong on this point, please correct me). She has only worn the brooch once, for a divine service at Sandringham on 1st January, 2006: