I did this when I ran out of current missions at 39. I didn't try for particular missions at the time, I was just desperate enough for any missions that I went back to talk to a few outleveled contacts and got a story arc. Since I like the story arcs, I did it a few times before I leveled up to 40 and my current contacts would give me things to do(no...I didn't level on the old missions, I helped friends with their missions for exp. I just like the stories).
One thing to watch out for, though....when I did this, the missions were grey, but the ambushes associated with the missions were my level.
Thanks for the clue that if you are persistent enough you can get the mission. The next time I am short things to do(which may be a while, actually) I'll go nag a contact.
Shae Firewarder
Lord knows half of my contacts I have outleveled, so this is a good oppurtunity for me to go back and hopefully maybe get a new contact that is my level so I can get some more xp. Thx for the good info.
Just a note...
If you dont want to get 'no experience' for the story arc, you might consider doing them when you have a Pile of debt. Go back, start your arc, and find someone appropiate to the mission level to join you for the story arc, and have them exemplar you.
In this way, you close your arc, and while exemplared, enjoy the challenge of the mission and reduce the debt you might have lying around.
Milk and Cream,
Kitten
Excellent idea, I think I'll do just that....
FWIW, it seems you *can*, at least under some circumstances, start a "missed" story arc by phone.
At level 38, my contacts are running short on missions, with mostly timed missions or "arrest 40 guys" missions, or against annoying enemies like the DE. So I started calling my contacts to see what they had, found an older one with a mission... against the DE, but what the heck.... 
And discovered that was the start of a lvl 35ish story arc I'd missed because I tend to avoid the DE, since they're so annoying to fight. I actually did get *some* experience, but everything's green or grey....
Whew.
Thanks for the info (although I had to dredge it up)... I love souvenirs, and the story arcs have fun writing.
To bad I have to still do invites for badge missions.
How to get Story Arcs you missed
Note that this ONLY works for Story Arcs, not for badge missions. It also will NOT work for the Hollows or Striga Isle special story arcs that have multiple contacts. This is for Story Arcs you didn't even start - ones you already started you can continue without having to do anything special.
Step 1) Outlevel a story arc without ever actually starting it. Oops! (Note: In my case I was at least 10 levels too high for the story arcs, I'm not sure if there's a minimum amount that you must have outleveled them by or not).
Step 2) Complete any Story Arcs you are currently in the middle of - make sure none are active (not just that you have no missions for them currently in your mission list, but that you aren't in the middle of a story arc AT ALL).
Step 3) Look in a guide and figure out which contact you had that would have given you the missed Story Arc. Some known guides are at http://coh.artphobia.net and http://www.rjcyberware.com/CoH/ContactNotes.phtml and probably others - try google if these don't work any more.
Step 4) Physically go to that contact (calling them will NOT work! You must actually go to them in person!).
Step 5) Click on them and see if they have text you can click on to look at missions, or if they just say they can't help you any more. If they have clickable text, it will lead to them offering the start of your missed story arc. If they just say they have nothing to offer you, go to step 6.
Step 6) Click on "Ask about this contact". Then click on "Talk about what else is going on." See if they now have text you can click on leading to a mission, or if they still insist on telling you to go bug someone else.
Step 7) Repeat step 6, over and over, until they eventually give in and change what they say and offer you a mission that starts your missed story arc! Shouldn't take more than about 15 times, although it did once take about 25 times for one particular contact for me.
Step 8) Do the story arc, but be aware that you will be fighting greys and you will get no xp for any of it. You will get the Souvenier at the end though!
And yes, I have personally done this, within the last few weeks. I went back and did all my tier 10 and tier 15 story arcs at level 27 because I hadn't bothered doing many missions in the first 20 levels. When I saw a random post mentioning this I didn't believe it at first, but I tried it and it worked.
Also, I have had old contacts that hadn't even given me their phone number yet still give me a story arc with this method, so the rumor that they have to be maxxed out to give you a missed story arc is not true AFAIK.
This also means it is possible to do all story arcs even if you do level too fast (see this post for more info on how it is that you can get all story arcs)