Women travellers will encounter little sexual harassment, though you’ll get more or less constant verbal 'approaches' from Cypriot men. This is common for both foreign and Cypriot women, but foreign women merit particular attention from these verbal Romeos. This can get rather tiresome, if not outright offensive. It is best to ignore the advances.
Solo women travellers should take reasonable care at rowdy nightclub resorts, such as in Agia Napa, where inebriated foreign males may be a nuisance.