Here's what I did to have no romance. I flirted with both and had "the confrontation" where you have to chose one. I chose Kaiden. Then, I left him to die on Virmire and POOF! Liara is not interested and Kaiden is dead.
Scenario 2: Choose to pick up Liara right before you go to Virmire. If you have flirted with Kaiden the entire time she will say something like "it's clear that you and Kaiden have feelings for each other and I won't stand in the way of that"... then let Kaiden die in Virmire.
Scenario 3: In Liara's second conversation, she mentions being interested in you. Just say the bottom "no" command. She ends it there. For Kaiden, also use the bottom options until he says something like "just got some wires crossed, Commander. But, I think I've gotten it straighted out." Romance over.
(not sure on this one) Scenario 4: Kaiden dead and Liara is pining for you... When she goes to comfort you say "no now, Liara"... if you are a renegade, you will completely shut her down. romance should end there... I think...
If you didn't choose those options, then it is hard to no romance without killing one of the options. However, I've never had a romance scene that I wanted to refuse (because if I don't want a romance, I followed the above scenarios). So, I have no idea if refusing sex will affect the picture frame.
Either way, it is not cheating if you move on. Your LIs in ME2 will not consider it cheating because of the time that passed. So, you are free and clear. It is not considered renegade to move on, IMO. Your former LIs have moved on as she will find out later.
That being said, some of my Shep's were loyal and some weren't. She shouldn't feel bad if a picture is on the desk, once you make your romance for another LI known, the picture will be turned down.