The last time I needed an upgrade from my employer (a while ago now, I'm self employed now) I made a very specific and detailed account of the problems I was having and why, and then we talked about it and I got about 1/4 of the way through the list before he realised I wasn't just asking for a nicer machine. The list was very, very specific - including wait times for things to compile and start up, and the amount of time lost by having to manipulate palettes in applications because my screen was too small, etc. Depending on which project I was working on at the time, I could demonstrate that I was spending sometimes nearly a whole working day in a week just waiting for things. It's a no-brainer justification for the person holding the purse strings if buying you a machine actually has a net financial (and productivity) gain.
They actually let me keep the 27" iMac they bought me in the end, but it's now my secondary machine as I bought a much nicer MacBook pro a couple of years ago :P