During your trip to Armenia you'll find the selection of gift/souvenir ideas a bit limited as well as very expensive.
The classic souvenir/gift item to bring back from your trip to Armenia is, without doubt, a rug. Rugs and weaving are part of Armenia's cultural heritage and there's no gift more typical or authentic that you can buy. They are indispensible home furnishings in any Armenia household. You'll find some stunning designs for sale. Prices can be very high, so don't be afraid to drive a hard bargain. At the same time, the cost reflects the quality - these are, after all, produced by master rug makers. Some are works of art. Be warned when buying rugs that, regardless of the price, it's forbidden to take old, antique rugs out of the country. Even if you buy a new one, you will be asked to present all the required certificates at customs. So make sure the seller provides the necessary paperwork.
Apart from beautiful, pricey rugs you may find the remaining choice of souvenirs somewhat limited and, once again, expensive. Even if you end up buying a token gift or decorative item, they often tend to be a bit tacky. Bear in mind that what's considered to be good taste or quality in the UK may not be the same in Armenia. That said, you should be able to find something for all tastes, including your own. You can pick up ceramic or stone sculptures, silver items, semi-precious stones and copper objects. You could also take home a bottle of Armenia's famous brandy. As with rugs, be careful what you buy, as it's forbidden to take antiquities out of the country. Make sure you get shop receipts for all items purchased.