[Stormcrow]

The thing about magic in Middle-earth is that it's not systematic. Therefore, coming up with a system to describe it kind of defeats the purpose.

Tolkien himself split magic up into two main kinds: Art and Will.

Art has to do with the act of subcreation, a term he uses in his essay "On Fairy Stories," and which I recommend reading to fully understand some of Tolkien's ideas. Basically, God is the Creator; his creations cannot themselves Create, but they can Subcreate: shape God's creation to it greater glory. When you make a gorgeous painting or statue, you are enhancing the world that the Creator made. When you tell a story so convincing that your audience believes in its world without effort, you are a successful subcreator.

All beings can subcreate and make Art. Elves and greater beings can do it better than others. When a man sings a song well, you might mentally imagine the scene being sung of. When a skilled elf sings a song (e.g., Finrod Felagund), he or she can actually make visions appear before the eyes of the listeners, and can actually manipulate their emotions. Sauron and Felagund have an epic song-battle, and Luthien sings Tol-in-Gaurhoth to the ground.

Art is best represented in GURPS as skills. Skills can simply achieve far greater things in the setting than they can in real life. A hobbit might learn the skill of Ropemaking really well, and make strong, light ropes, but an elf has even more skill in Ropemaking and can make ropes that are stronger, lighter, can untie themselves when called, and which reflect any light around them. And a hobbit who spends enough time with elves who teach him Ropemaking can learn to make ropes like this too: it's not a special ability of the elves; it's just a consequence of their greater lore. That elf sitting in front of you probably had a spare century to devote just to Ropemaking. But a dedicated hobbit could learn it too.

Will is what powers wizardry and sorcery, two words which more or less mean the same thing but which tend to get used for the good guys and the bad guys, respectively. Sorcery is about dominating the minds and wills of others; wizardry is about dominating the natural world. More or less. These aren't strict delineations.

Telepathy is a thing in Middle-earth, though not by that name and not as "mind powers"; we see a lot of it in LR. So are visions, dreams, and prophecies. These are nearly always caused by some power greater than oneself, messages delivered "telepathically." There's even a scene on the journey home where the great people sitting in camp converse with each other purely by thinking. This is their great Will in action.

Curses and oaths are also prominent, and efficacy in them is an act of Will, along with the stature or authority to impose it. Isildur could curse a whole people with his Will because he possessed the right to do so.

Magic by Will is best represented in GURPS by advantages and spells. Wizardry and Sorcery are regular GURPS spells, but you have to carefully curate the available spell lists. It's probably best to have to learn each spell individually; general skills like those used in ritual magic aren't really appropriate. Middle-earth is high mana (despite what people usually think); you can cast spells without possessing Magery, and most spell-casters do, but knowledge of spells is very limited.

As for magic items, those are mostly made through Art. This is a place where Art and Will often coincide, as a magic item may be made through Art to focus will. The Rings of Power do this; they're all about dominating others, and, in turn, being dominated by Sauron. The Three Rings are about Will too: Galadriel uses Nenya to preserve her kingdom from time by her will; Gandalf uses Narya to inspire and strengthen the wills of others.

That's just a start. There is plenty of work to do to turn all that into a workable system.