I finally managed to get an environmental map working in Blender to make a reflective object. I found the standard tutorial for envmaps to be a little confusing, but this (scroll down) proved to be very useful in providing a simple series of steps for the basic effect. I still need to explore multiple recursive reflections, which were introduced in the last few releases of Blender. And of course, a reflective sphere is one thing, but actually making convincing reflective real-world objects is a different story. Back to work.