How to take super close ups?

My old Sony Cybershot DSC-T5 has this feature that allows me to take amaaazing extreme close ups, i'm talking within an inch of the object here. However in most other digital cameras, at least most compact ones, they don't seem to have that function. So I'm just wondering how can I take closeups like the ones from my cybershot with other compacts and slr, or am i completely deluded and all cameras now have this function?