No entry reservation. All cave access is by ranger-guided tour, and tickets are required.
Centennial Trailhead parking: Overnight parking without a camping permit is prohibited, and permits are not issued just for parking.
Backcountry use permit: Free, required for all backcountry campers and picked up at the visitor center information desk. Horseback riders need a free permit too.
Cave tour tickets: You need a tour ticket to enter the cave. About half of tickets are sold ahead on Recreation.gov. The rest go first-come at the visitor center on the day of the tour and can sell out quickly.