Yeah, Southern Methodist University does provide scholarships based on merit. Here are some of them:

President’s Scholars Program
Total Worth: full tuition
Eligibility: full tuition
Separate application needed: No

Nancy Ann and Ray L. Hunt Leadership Scholars Program
Total Worth: 42000
Eligibility: 42000
Separate application needed: No

SMU Distinguished Scholarship
Total Worth: 20000
Eligibility: 20000
Separate application needed: No

Southern Methodist University provides aids at an average of 43715 per student meeting 87% of students need. 100% of students with need receive financial aid at an average of 19090 need-based grant. They also provide other scholarships including Robert H. Dedman Scholarship for North Dallas High School and Stars on the Rise.