They don’t have any automatic aid that I know of except for National Merit finalists. Those students must get in and name UM as their first choice, and then they’ll get no less than $16,000.
The main scholarship UM has is the Presidential Scholarship which ranges from $8,000-$28,000 per year. You’re automatically considered for it when you apply, so there’s no separate application. The best way to increase your chances of getting the scholarship and getting a lot of money out of it is to have very high test scores (a 33+ on the ACT or the equivalent of the SAT, and UM superscores and doesn’t require the writing sections for each test). Miami also likes to see a very high class rank (at least the top 10%), and getting straight A’s also helps. Scholarship-wise, it seems like an applicant’s academic achievement comes first, and extracurriculars are secondary. Of course, all of UM’s full tuition/full ride scholarships are extremely competitive, and it eventually is just a crapshoot.
It’s hard to predict what your son will get because UM has no clear-cut answer as to how they award scholarships. You can see what stats got students scholarships in this thread: http://talk.collegeconfidential.com/university-miami-florida/1709491-university-of-miami-class-of-2019-early-action-results-p151.html
I’m in a very similar situation as your son. I’m expecting little need-based aid and trying to earn as much merit money as possible when I apply this fall. I’m not willing to take out loans for undergrad so my gut feeling says that I’m not going to be able to attend UM if I get in.