TESOL Connections just posted an interesting article about students assessing their own writing. You can find it here. I think it's a great idea to start early on with self-assessment, not just to be used with advanced students. It will encourage students to read and understand the rubric (does anybody else have this problem??), and it will also encourage self-reflection. This article is only about writing, but it's also possible to use with speaking assignments if they're recorded and made available to students to view (I use YouTube).
I often include a written portion to self-assessment assignments. For example, I provide a copy of the rubric for students to assess themselves and on the other side of the paper, I include a space for students to write about (A) what they did well, (B) what needs more work, and (C) the grade they think they should receive and why. I really think the written portion is just as important as the rubric portion. Students don't just have to decide what they did, but they also have to justify it. It's also a good way to track growth of the learner. If you use portfolios, these reflections could also be included there.
Are there any other ways we can use self-assessment to encourage and monitor language learning?