I have no information about the diamond and gold bracelet worn by Queen Letizia on the picture posted by Maridje.
The other bracelet (the one worn by Queen Letizia at the Danish festivities) was indeed worn very frequently by Princess/Queen Letizia. I don't know when she received it, but in the early years of her marriage, if not at her wedding itself. It has a modern design of vertical bars, like a modern fringe. As Letizia has always been very slim, the bracelet (which looks to have a rigid frame) is often worn by Letizia high on her forearm, where flesh is bigger, rather than at wrist level.
Princess Letizia of Spain attends King Juan Carlos 70th Birthday Gala Dinner on January 09, 2008 at the El Pardo Palace near of Madrid. (Source: Carlos Alvarez/Getty Images Entertainment)