"In many fantasies, particularly in very popular YA fantasy series, magic seems…well…magical. Things happen for no reason beyond the quick application of a magic wand. Is it possible to make magic systems consistent? Who are some authors who’ve managed to achieve this?"
The first question was left out of the description: do you want to make your magical system consistent? What are the advantages and disadvantages of it?
The obvious disadvantage is that it makes it so much less magical. Magic is unexplained causality. Drinking willow-bark tea for your headache used to be magic. Nowadays, magic tends to be "stuff that people used to think would work, but which science has debunked, so that if they work at all, it's sorcery -- trafficking with evil spirits." But part of the flair, the wonders, the marvels, is its unpredictability.
The obvious advantage lies in plotting. You can make it clear what your characters can and can not do so that your readers neither assume that the fight will be a snap, nor refuse to believe that your character can actually win. Rhetoric can pull this off, but consistency helps too.
I blame Ursula K. LeGuin. Tolkien made his magical characters supporting ones, and not even human at that, and Robert E. Howard set Conan and his ilk against the sorcerers in his sword and sorcery. But LeGuin put the magic in the hands of the main character, and not safely encapsulated in a ring, or an enchanted sword, which could have its own unfathomable depths.
System is quite useful, but on the whole, I find a broad strokes approach to be best. If the reader knows the sorts of things your wizard can do, and knows vaguely the price he has to pay -- the steeper the more powerful the wizardry is, the character can be contained within the bounds of plot
part of bittercon.