Looks good - and expensive (well, the 2nd one, certainly - fiddly gem setting.. eek) :)
There's two things I miss...
1. Caustics
Try enabling caustics on your main light, or create a seperate light for caustics generation. In the first image that should give a nice parabolic arc below the rings, and in the 2nd image it should give nice spots of light from the little gems.
See also Brian's tutorial:
http://brazil.mcneel.com/blogs/tutorials/archive/2008/12/12/jewelry-rendering-with-brazil-for-rhino.aspx
2. Glint/glare
This is something that I miss in most renders, while it can add a lot. Basically it's just a post effect that adds a light glow / star shapes around the very bright parts. The way you get those bright parts is by creating some banner of 'light card' in the scene (basically just an object with a very bright surface) which then gets reflected/refracted. Typically at the position of the lights, but you can move it wherever looks good (something you can't do in real life so easily without affecting the illumination). You can then either add Rhino's glow effect, or save to an HDR/OpenEXR image and process it in post.
Because tiny little glints often get lost in anti-aliasing, you could even render at a higher resolution, don't anti-alias, apply the glow/glare/star filter, and then size back down.
Not sure if you're familiar with DiamCalc..
http://www.octonus.com/oct/products/3dcalc/standard/
..but the examples show the effect, and you should be able to toggle it within the demo program. It really has a pretty big impact, but as with all such post-effects, you *can* overdo it :)