How can I make cookies without any sugar? I'd like to try making some sugar-free cookies, which means no refined or "natural" sugar (honey, came syrup, etc.).  I'll be trying to use stevia instead.

The obvious problem is that sugar is very important to cookies structurally, not to mention caramelization.  Even if stevia were to caramelize, there won't be enough in the recipe to be sufficient for the taste.

So, are there any other agents I could use to counter these problems?

Related: Does Splenda caramelize?  (No.)
No, there are no other agents. Caramelization is literally sugar in a certain state. If you remove all the sugar, you cannot have a caramelization taste. You can make cookies which don't taste caramelized, of course. 

As for the "important structurally" part, it depends what cookie you are trying to make. If you want to achieve the texture of a sugar-rich cookie, this is again impossible. Out of all edible substances, only sugars behave like sugars when baked. 

You can however use other fillers to get a different type of cookie. A shortbread cookie (like pie crust, but in cookie form) with stevia shouldn't taste that much different than a shortbread cookie with sugar. Nut flours or nut butters will give you some very good fillers so you can make a cookie with some bulk without having to use too much flour. 

The result will never look and taste like a standard American chocolate chip cookie, or its relatives but will certainly deserve the term "cookie".