Don't be dissuaded by the high schoolers you see at the local mall food court who try to climb into the trash bin, or who try and see who can fit the most fried shrimp in their mouths. Rest assured, there are many responsible, competent babysitters of high school age in your community. Posting a flyer on each of the bulletin boards at the local high school may require you to sort through dozens of teens of varying acceptability. Like any search for quality childcare, you have to choose your target audience wisely.
Request the class roster of students enrolled in electives pertaining to early childhood education and care from the local high school. Choosing an elective, rather than required course, will weed out the teens who have no interest in small children. Privacy laws vary between state and district, but most public high schools will be happy to provide a list of names after you explain you're in the market for a qualified teen babysitter.
Call your local Red Cross chapter or YMCA branch and ask for a list of high school students who have successfully completed babysitting certification. The course teaches basic first aid and care of children to high school students over a several-week period. Upon completing the course, each student receives a certification. If possible, ask that the list include the town where each student lives. They may not disclose the teen's full address but having a sense of where the student lives could save you from calling a babysitter who's 45 minutes away.
Contact the high school athletics department about upcoming youth clinics coached by high school students. Many high schools offer sports camps or clinics, especially during the summer, that will let your kids interact with several high school coaches. Take note of which high schoolers you find particularly responsive and mature, and approach them after the clinic about babysitting for your kids. Not only is this a good way for you to see potential babysitters in action, it also gives your kids a chance to become familiar with the high schooler before she arrives at their door.