Even I didn't know how much Tolkien drew, but he was actually quite good. So, the linguist and author, as part of his world, decided to create a system of heraldry for the elves. It's kind of complicated, but really cool. For more in-depth stuff, check out J.R.R. Tolkien: Artist and Illustrator, by Wayne G. Hammond and Christina Scull. I love that book.
There's also some made-up heraldry in the Art of the Fellowship of the Ring book, because the Weta folks needed some to put on banners. Notably, a device for Galadriel is there, where there wasn't one made for her by Tolkien.
Anyway, here goes. For female elves, their heraldry would be within a circle, while men would be in a diamond. A device that's created for an entire line would be in a square. Most devices are symmetrical, with Finrod's being one of the exceptions. According to Tolkien's notes, an elven prince would have four points reaching the outer rim of the device, kings would have six or eight, and really important folks could have 16.
Idril: "...the twelve flowers or points reaching the edge of the circle may reflect Idril's position as a king's daughter."
Earendil: (shown here in living 3D, since I couldn't find the original) Notably, Earendil's device shows a Silmaril (jewel) that reflects the way he sails the sky as a star. Elrond's device in the Art of FOTR is based on this device.
Gil-Galad: The elven king (note: eight points touching edge) who brought up Elrond. Gil-Galad's costume for the opening of FOTR was based on his heraldry. See below.
Finwe: With sixteen points, Finwe has one of the highest statures among the heraldry - he was High King of the Noldor in Aman. This is the device for his house, however. Note the fact that such a fiery emblem is for the father of Feanor, a fiery figure.
Elwe: He has merely eight points, denoting his position as a king. It is interesting that, since he stayed in Middle-Earth instead of returning to Aman, that his device has stars, also mirroring one of the devices of his daughter, Luthien.
Finarphin: The father of Finrod Felagund. Tolkien expressed that most likely this was very close to the one he had in mind for Finrod. The later one for Finrod was made by Men.
Fingolfin. I don't know much about him.
Woot! Melian, a Maia, mother of Luthien Tinuviel. Tolkien created this absolutely gorgeous device for her - it's really complex because she's a Maia - she's really important. There are stars present, which is reflective of her nature. The complexity is similar to Luthien's below.
For the sake of precision, we'll call the top device Luthien 1 and the bottom Luthien 2. Since Tolkien considered the story of Luthien and Beren similar to that of his love story with his wife, he probably considered drawing these an act of love (I know I would, but that's just me.) My personal favorite is the lower. The top one has twelve points touching the outside (she's a really important character), and I can't count the number on the second. There are twelve petals in the center, however. Luthien 1 reflects her father's device.
Interestingly enough, there's an elven device for Beor, the father of Beren. He spent a fair amount of time among the elves, but still, it's a bit weird.
Finrod Felagund. Tada! A tad boring, no? Nonetheless, it's important because he was so compassionate towards the human race. Here's a picture of him meeting them for the first time:
