The writing system used for Quenya and Sindarin in J.R.R. Tolkien’s Middle-earth is Tengwar. Tolkien designed the Tengwar, also called the Fëanorian characters, as an alphabet used for several languages in his legendarium.
Tengwar is especially associated with the Elves and appears in famous inscriptions, including the inscription on the One Ring. That inscription is written in Tengwar letter forms, although the language represented is Black Speech rather than Quenya or Sindarin.
Tolkien’s system is not simply a decorative alphabet. Its letters, or tengwa, are organized according to phonetic features, and the system uses tehtar, marks placed above or below letters, to represent many vowels. Different languages can therefore use the same script with different conventions.
Readers sometimes confuse Tengwar with Cirth. Cirth is a separate runic writing system associated especially with the Dwarves, while Sarati is an earlier script in Tolkien’s invented history. Angerthas refers to expanded rune alphabets based on Cirth.