I have to polish a narrow strip of granite that runs as a border along side a strip of flamed granite. The polished granite strips are about six inches wide. How do I hone the polished granite without honing the flamed granite?

The situation you describe is becoming increasingly popular. It seems designers and architects are mixing different finishes together making it very difficult to restore the polished portion. The only way to restore the polished granite without touching the flamed is to use a hand polisher equipment with a 3-5 inch drive pad. I would tape the edges of the flamed granite with duct tape. If it is possible, try to place a 2x4 even with the polished granite covering the flamed granite. You are creating an artificial edge. You may need to construct braces so the 2x4 stays in place.