Searching Google for setting unsupported resolution on mac returned an application called SwitchResX, which is the kind of solution I have been looking for a while. I use 2 2560x1440 monitors at work but the problem arises when I'm working from home - Macbook Air supports the resolution of 1440x900. Therefore I connect it to an HD screen - the TV - and work with a wireless keyboard & mouse.
When doing so, the screen is mirrored on laptop and TV - where I've noticed that Mac also sets the resolution to 1920x1080 - which is not supported from Display settings. That was the 'aha' moment.
Now I'm not using 1920x1080 on Macbook Air but instead 1680x1050 - which works quite well, and I'll be purchasing the full version of SwitchResX.