Right, other than the very competitive Banneker/Key scholarships (https://www.financialaid.umd.edu/scholarships/banneker_info.html), the awards may be rather small or not available to OOS students.
However, the OOS sticker price is about $40K/year. Compared that to a private school such as Rochester, where the sticker price is ~$70K and the average merit award seems to be about $14K.
To count on a net price significantly lower than Maryland’s ~$40K, assuming you don’t qualify for much/any n-b aid, you may want to consider somewhat less selective schools such as Alabama that offer large automatic merit scholarships for qualifying stats. Or, consider your in-state public options. But at many fairly selective private schools, most merit awards seem to top out at around $20K-$25K. If you see “full tuition” or “full ride” scholarship programs at a selective/prestigious school, expect the competition to be very tough.
http://automaticfulltuition.yolasite.com/
http://competitivefulltuition.yolasite.com/