Regardless of religion differences, local people have rather warm and friendly attitude towards their Muslim neighbours. And maybe that's the reason that lately Armenia has become a popular tourist destination for Arab tourists.
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A t-shirt and shorts or skirt just above the knee is acceptable. Most of the locals will be wearing trousers. For monasteries, women are meant to wear a dress and cover their heads. Men should wear long trousers.
U.S. citizens should continue to exercise caution near all international borders between Armenia and Azerbaijan and avoid travel near the Nagorno-Karabakh conflict zone and line of contact.