Schmidt earned the highest finish by a Tar Heel in an individual event, crossing the line second in the 800 meters with a time of 2 minutes, 8.47 seconds.
Flanagan placed seventh in the mile with a time of 4:45.25, edging out Jill Snyder of Wake Forest by four one-hundreths of a second (4:45.29).
UCLA won the 2001 NCAA Indoor Championships with 53.50 points, followed by South Carolina with 40. Clemson and Arizona tied for third with 30 points.
Arkansas, Colorado, Missouri, Texas-El Paso, Houston and North Carolina rounded out the top 10.
The Tar Heels finished with 19.33 points in the competition, just 4.67 points out of the top five.
North Carolina last placed 10th at the indoor championships in 1999.
Seniors Ola Sesay and Joy Ganes walked away with All-America honors. Sesay finished eighth in the long jump with a leap of 20 feet, 9 1/4 inches.
Ganes tied for the eighth spot in the high jump with a mark of 5-10 3/4.
Schmidt and Flanagan, along with Beth George and Edi Ntuen, already earned All-America honors from a second place finish in the distance medley relay on the first day of competition.