making very fine cuts with the 40AMP/50AMP torch

What consumables would I replace if I wanted to make very thin, fine cuts on thin steel with my 40AMP/50AMP torch?

Assuming you have the S45 torch. There are tips with smaller orifices available, Standard is .8 or .9 mm.
I have seen them down to .6, smaller orifice, finer kerf but less power capabilities.
If you looking for smoother cuts, try using a “new” tip, raising the air pressure slightly (confines the plasma stream). Or using less current.
Travel speed and consistency (steadiness) has a big effect on how smooth the cuts are.
Mark might have some suggestions also.

The current tips DO offer about as fine as cut as practical.

Actually I am not wanting to cut with it. I am doing some art work and I found that I could make some very interesting surface "etching" with the current nozzle. However, on thin metal, the margin between etching and cuttng is very slim with the current nozzle. So, I want something a bit more delicate. And yes, I have the S45. I checked with my local welding shop and they wanted to know what brand the S45 torch was. What is it? And, where might I buy these tiny nozzles?

Trafimetusa.com or google for trafimet S45 consumables. You will have to weeds though a number of sites. But they are out there.

Its hard on cons, but to etch, just don't use the ground clamp and the torch will not cut.

Without the ground clamp the torch does not do what I am calling etching.

Anyway, I ordered some .6mm nozzles. I am told that they are rated at 5 to 15 amps. What will happen if I go over the rated amps? Will I break something???

Where did you order them from?

Keep in mind, the units minimum amps is 20.
What it will do is blow the bottom out of the consumable, or at least widen the hole.

Since I have no idea what I am doing,, I probably got too small of nozzles. I will turn it down to 20 and hope that is not too much more than 15 amps. As long as it does not screw up my torch it will not get too upset if it burns the hole in the .6 nozzles. Oh well they were only $14 with shipping on Ebay. That is the only place I could find them.

As Ray mentions, consistency is all important. This cut was done with a constant feed, no wavering and it turned out pretty nice.