Mariette Schrijvers, a 58-year-old teacher from Holland, said she would like to see Dutch officials visit St. Maarten more often, saying the relationship on both sides could be warmer.
"The crown can also get to know more about education, medical care and the physically challenged in St. Maarten during their visits," she said.
The couple is expected to also visit Saba, St. Eustatius, Bonaire, Curacao and Aruba.
The Dutch colonized the islands in the 17th century, and they once formed part of the Netherlands Antilles.
In 2010, St. Maarten and Curacao followed Aruba's lead and obtained greater power of government and began collecting their own tax revenues. Meanwhile, the smaller islands of Saba, St. Eustatius and Bonaire became Dutch municipalities.
The islands' people are Dutch nationals, and Willem-Alexander is their head of state, overseeing foreign affairs and defense.