Both destinations are served by Chandigarh Airport (IXC). Since there's no flight route between them, the best way to travel is by road.
Chandigarh
Fly to Chandigarh Airport (IXC), then travel by road to Chandigarh. Taxis, buses, and private cabs are available from the airport.
Shimla
Fly to Chandigarh (IXC), then travel by road to Shimla. Local transport options include taxis, auto-rickshaws, and state buses.