The number and variety of literary devices that writers can apply to their work is so great as to make a complete and exhaustive compilation of them almost impossible, practically speaking. I think this is the case even in a shorter poem such as Shakespeare's Sonnet 116.
That being said, one device that I find particularly noticeable and attention-grabbing is Shakespeare's use of repetition, specifically on particular words. This effect can be seen in each of the poem's second through fourth lines, with the words "love," "alter," and "remove":
Love is not love
Which alters when it alteration finds,
Or bends with the remover to remove.
This use of repetition has the effect of adding added emphasis to these specific words within the verse. Thus, even beyond the normal stressed-unstressed dynamic of traditional meter, this adds additional levels of stress on entire words, separate from the syllables that form them.
In addition, you can point towards various poetry-specific devices that would be common to all sonnets (given their formal structure): this poem, for example, has a consistent meter (being iambic pentameter) and a formal rhyme scheme (being abab, cdcd, efef, gg). Beyond these formal elements, you can also point towards Shakespeare's use of devices such as consonance, repeating the same consonant sounds. For example, in the poem's very first line, you can observe at least two separate examples of consonance working together with one another. Thus, "Let me not to the marriage of true minds" features repetition of both the m sound and t sound (alongside what looks like a possible third layer of consonance given the close proximity of the r sound linking the words "marriage" and "true").
All this being said, however, be aware that there might be an open question as to the degree to which Shakespeare used imperfect rhymes in this poem. After all, at first glance, this seems to be a common effect. Consider Shakespeare's linking of the words "love" with "remove," "come" with "doom," and at the very end, "proved" with "loved." However, here it is important to keep in mind that Shakespeare died over four hundred years ago, and four hundred years is a long time for linguistic drift (speaking in terms of the pronunciation of various words). With this in mind, it is worth questioning how these various words were pronounced in Shakespeare's own time, rather than our own. Perhaps some of these imperfect rhymes may have been full rhymes after all.