Since we couldn't find much information about travelling as an unmarried couple in Iran (apart from that it's possible), I just wanted to share our experience with other couples who are planning on going. We travelled for two weeks in Iran this summer, and had an absolute whale of a time in this fascinating, diverse and endlessly friendly country.
Visa
First of all: the visa. We - young couple, both Dutch nationals - applied at the embassy of Iran in The Hague. Print and fill in the visa form before you go, it saves a lot of time. You should bring two passport photos each, but there is a photo booth in the embassy in case you forget to bring them. On the visa form, you have to check a box whether you're married or single. Also, the relationship with your fellow traveller is asked. We chose to be honest and wrote: "single" and "unmarried couple". Although it took 5 weeks to be issued, there was no problem, no questions asked. To get the visa in The Hague, you have to go to the embassy yourself, but they do mail the visa to you. Cost us 10 euros for two passport. You do not need an invitation, although visa agencies will tell you you do!
Staying in a hotel as an unmarried couple
We stayed in hotel rooms together for two weeks, nobody asked us whether we were married or not.
Talking to Iranians
Let's be clear: Iranians are among the nicest and most welcoming people we've ever come across. People approached us all the time. Women would speak to my girlfriend, men would always talk to me. Shaking hands between men and women is very uncommon. We decided in the beginning to say that we are married. If we were Iranian, we probably would be married, so we thought that would be the easiest. People do ask, and looking back, I would probably suggest you can be honest about not being married: people in Iran are very aware that this is common in western countries. We got invited to a family picnic and someones home for dinner. It's a great way to get to know the country so do say yes if you get invited!
Public transport
City buses and metros do have a 'women only' section. Men are not allowed here, but women are allowed in the common section (ie there is no men only section). In intercity buses men and women are mixed, and you can sit next to each other. But as a man, you are expected not to sit next to a women you do not know.
**Clothing: **
It depends greatly on where you are in the country how conservatively women should dress. In some areas like Kashan or Qom, my girlfriend would feel more comfortable wearing a black headscarf, not showing much hair, while in many areas in Tehran, you can show a little more hair.
Women: it's the law, so do read beforehand what Hidjab/Hejab means and bring different sets of clothes so you can adjust to the local customs.
Men: (probably) not the law, but shorts are not acceptable in Iran and it is very uncommon to wear flipflops outside.
Money
You'll already know this, but I'll say it anyway: no, there is no ATM anywhere in Iran you will be able to use. Bring CASH (USD or Euros). It feels weird walking around with a pile of cash in your backpack, but we did not feel unsafe at any time. People know that travellers bring cash, and still robberies don't seem to occur, at least not often. Do not change money at the exchange office at IKM airport on the ground level. The upstairs offices have much better ratings. At least, when we were there.
Crossing the border to Armenia at Nordooz
After Iran, we spent 10 days in Armenia and Karabakh. Crossing the border at Nordooz was easy, took about 30 minutes. But prepare yourselves, the taxi drivers at the other side of the border in Armenia are pretty hostile. While hassling over prices in Iran is not common or necessary (we were refused to pay for a taxi twice), it is in Armenia.
Alright, hope this helps!
