Female travellers in Zambia will generally not encounter gender-related problems any more than they might in other parts of the world. In fact, women travellers say that compared with North Africa, South America and many Western countries, Zambia is relatively safe and unthreatening; friendliness and generosity are encountered far more often than hostility.
Due to Zambia having a small population of European origin, women travellers can meet and communicate with local men – of any race – usually without being misconstrued. That's not to say that sexual harassment never happens, but it's certainly not the prevailing attitude.
Be aware, though, that when it comes to evening entertainment, Zambia is a conservative, male-dominated society. Even in bars where women are ‘allowed’, cultural conventions often dictate that you don’t go in without a male companion.