Miniature, fully functional 1/3rd scale replicas of a Cadillac were made for the British Royal family of Siam, Norway, and one for a grandson of the founder of Cadillac.

the one built for the royal family of Siam above, the other for Norway below.
Interestingly, Prince Chula was the great-grandson of the much romanticized King Rama IV (1851-1868) of ‘The King and I’ fame.

The brain behind the little car was Frederick S. Bennett, an Englishman who played a pivotal role in establishing Cadillac’s success in the UK.

 As a Cadillac dealer across the pond, Bennett’s greatest challenge was emasculating prevailing public opinion that American products weren’t built to last. His persistence finally paid off in 1909 when Cadillac became the first American auto manufacturer to receive the Royal Automobile Club’s prestigious Dewar Trophy after a rigorous interchangeable parts test in 1908.

 One of the finest and earliest miniature cars, a one-third size Cadillac built in England before the First World War, built in 1912 by Lockwood and Co of Islington, north London, the car was exhibited at the 1913 Paris motor show.

Though weighing nearly 400lb, the Baby Cadillac was capable of about 15 miles on one charge at speeds of up to 12mph. Driven along Pall Mall that year as a publicity stunt, the little car attracted royal attention and was bought for £62 by Queen Alexandra, wife of Edward VII, who gave it as a gift to her grandson, Prince Olaf of Norway. Though still owned by the Norwegian royal family, it is on permanent loan to the Norsk Teknisk Museum in Oslo

While the Norwegian miniature is known in informed circles, two other examples were built, one of 1916 vintage going to the Siamese royal family as a present from Cadillac. It was certainly driven around the royal palace grounds by the young Prince Chula, who became well known on European racing circuits in the 1930s, and is believed still to be owned by his descendants.

The third Baby Cadillac went as a fifth birthday present to Wilfred Leland, one of the Cadillac founder's family – possibly as close to royalty as the US gets

http://www.telegraph.co.uk/motoring/2724262/Right-royal-fun-in-a-Baby-Cadillac.html
http://www.cocgb.dircon.co.uk/cadillac_spectacular.htm
http://www.independentcinemaoffice.org.uk/films/the-big-smoke
http://grofjardanhazy.tumblr.com/post/62235955433/a-baby-cadillac-bought-by-queen-alexandra-as-a
http://www.aacalibrary.org/articles/antique-automobile/f-s-bennett-and-the-three-baby-cadillacs/
http://thornews.com/2012/03/18/royal-journeys-1905-2005-norwegian-art-exhibition/
http://www.royalcourt.no/nyhet.html?tid=115905