Amur Falcon

That's what I was thinking it was, based on pictures and the name sounds really familiar like that's what our guide called it. Glad you agree!

http://www.butbn.cas.cz/hajek/africa/Pho...
http://ibc.lynxeds.com/photo/amur-falcon...
i think it's better waiting for Liam's confirmation..

There's many species of them and are about the size of a crow.

Ok it actually could be a peregrine falcon. It looks similar to the ones where I live. They are known to be all over the world so that could be something to look up.

All I can find is the Eurasian Sparrowhawk, but it doesn't get into South Africa

Of coarse I'm not sure if their around your area but that's first thing I thought.

Looks like a sparrow hawk