Isner, the top seed and defending champion, beat South Africa's Izak Van Der Merwe 6-4, 7-6 (2). Sixth-seeded Harrison was ahead 6-4, 3-0 when Germany's Benjamin Becker retired with an injury.
Lleyton Hewitt of Australia and 2009 Newport champion Rajeev Ram will meet in the other semifinal.
Isner is looking to become the first consecutive champion on Newport's grass courts since Greg Rusedski in 2004-05.
- Ryan Harrison
- John Isner
- Izak Van Der Merwe