Swazi Airlink operates out of Matsapha International Airport, north of Manzini, and flies to Johannesburg, Maputo, Harare, Lusaka, Dar es Salaam and Nairobi. Schedules and tickets often refer to the airport as Manzini.
Swaziland has 11 border posts with South Africa and one with Mozambique, and the smallest posts close at 4pm or 6pm. There is a bus service from Mbabane to Maputo in Mozambique, and buses ply the roads between Mbabane, Durban and Capetown and Jo'burg to Mlilwane. Minibus taxis also run between Jo'burg and Mbabane, but for most other destinations in Swaziland you'll have to take a minibus taxi to the border and then another from there to the nearest town, then change again. This can take time.