Luxury hotels are boosting efforts to cater to their littlest guests. Hotels say they are responding to increasing demand for kid-friendly services from travelers, who are bringing their wee ones to high-price hotels in never-before seen numbers.

The rise of later-in-life childbearing—when more couples have the money to travel—is playing a role. So are baby boomers who organize, and often pay for, trips with children and grandchildren.