Originally posted by: *Jane*
As the Trace breaks when one turns Seventeen, there is no way anyone is able to detect magic of any sort, that includes apparition from those older than Seventeen. Like Remus Lupin said, "It's impossible to track anyone who Apparates, unless you grab hold of them as they disappear!"
Quote from Chapter 11, page 205, US Edition of HP and the Deathly Hallows.
An Apparition license is like a driving license, in more sense's then just one. A person is capable of driving and certainly can do so but without a license it's illegal meaning, in some cases, they have to spend time in prison for it. This motivates people to get a license and to actually study up on the basics. It's just a precaution the ministry put up to make sure everyone does safe Apparition but there are of course, lawbreakers that just won't.
PS: Hermione's wards didn't have anything to do with the detection of their magic. It had to do with making sure that if anyone was around the surrounding area, they wouldn't be able to see or hear them and to "repel" them in some way form or another so whomever it is won't come near their area.