One company is Classic Africa, which arranges small group trips to wildlife camps in Botswana, Namibia, South Africa, Zambia, and Zimbabwe. The firm was founded by Margaret and Pierre Faber, who provide custom trips for about 500 clients a year
I have twice gone on safaris in East Africa (photos from my Kenya safari). They have been absolutely wonderful experiences getting to see vast expanses of natural wildlife is like nothing else I have done. They are costly but if you can afford it they really are quite amazing. While the TV shows exploring these location don’t equal a visit they are pretty great also.