Hookah and tea are an old pair. Hot black or herbal tea refreshes the palate between puffs, and many Yerevan lounges serve mountain herb tea with thyme, mint or rosehip.
Cold drinks work too: lemonades, especially tarragon or citrus, go well with fruity mixes, and still water is the best partner for mint. Avoid very sweet sodas, which make the flavours feel heavy.
Many people avoid combining hookah with a lot of alcohol: both can cause dizziness, and together the effect is stronger. If you drink, take it slowly and keep water on the table.