The queen and Scottish First Minister Alex Salmond had a brief formal meeting at Holyroodhouse, her official Edinburgh residence. Salmond, head of the Scottish National Party, received his Royal Warrant, allowing him to form a government.
While Salmond is the fourth First Minister since 1999, he is the first from the SNP. He has protested swearing allegiance to the queen.
Scotland and England became separate countries under a single monarch in 1603, when Elizabeth's ancestor, James VI of Scotland, succeeded his cousin, Queen Elizabeth I, as James I of England. A century later, the Union of the Crowns created the United Kingdom, which also includes Wales and Northern Ireland.
The SNP would like to wind the clock back with an independent Scotland.
"I am sure her majesty can deal with this situation as she has dealt with many before," said historian Michael Fry. "Before 1707 and after 1603, the monarch was a composite monarch of independent countries."