Here is what I have always recommended, based on years of experience, and thousands of breedings. Sometimes it does not matter, but the best choice is to leave the female alone, and bring the male to the female's cage. Why ? If you work with chameleons long enough, you will notice that the male of the species is more quickly consumed by an opportunity to breed than a female. In example, if you bring a skittish male to a female's cage, he is often likely to lose his skittishness towards you once he sees the female, and start head bobbing, than a female is to lose her skittishness if being moved to the male's cage. Put another way, male chameleons demonstrate a much more one-track-mind than females. Female chameleons, if handled or moved to the male's cage, will often show a longer-lasting skittishness to being moved, to the new cage, etc., and now has to start feeling sexy when seeing a male chameleon on top of it all ! Conversely, the male can show his sexual desires while still on your hand, while outside the female's cage but seeing her ! Females almost never show a sexual relaxation (ie "one track mind") during movement from one cage to another, and will show stress at being handled, moved, and now confronting a horny male. Point being that you would like to keep the stress factors minimal on the gender that is making the decisions.
The second reason is that you need to minimize non-compatible unions and the injury that can result. Consistent with the above, it is the female that needs to be ready, as the male is always ready. By leaving the female alone, you are keeping the outside disturbance to her at a minimum. Seeing a male perched on your hand will certainly get her attention. You can gauge her reaction before you ever allow the male to actually enter the female's cage, thus avoiding a non-compatible union, or what we call here "date rape", which some aggressive males will attempt. Bringing the male to the female, and looking for her reaction before he actually is allowed to make contact, is safer that putting the female into the male's cage, where unwanted contact can occur quickly, and you find yourself having to separate animals in physical contact with one another, often by mutual bite.
With all that we know, from years of observation, there is just about no circumstance where bringing the female to the male's cage makes more sense. It introduces far more risk, and is more likely to interfere with a natural reaction on the part of the girl. Good luck.
