I don't actually know. I'm sure our present queen must admire Elizabeth I but I can't remember her ever mentioning her in a speech. I can imagine the queen being very interested in history, particularly when it comes to the monarchy, and http://www.royal.gov.uk/, the moarchy's website, has a page on Elizabeth I - see http://www.royal.gov.uk/HistoryoftheMonarchy/KingsandQueensofEngland/TheTudors/ElizabethI.aspx