Near miss on Open Road 6c, I was the belayer in this instance with climbing partner on lead. All draws were preplaced as I had led just beforehand. The route starts by climbing a ledge to the right of the route and then traversing over to the left to where the line continues up. First bolt is off to the right out of the way so second bolt was pre clipped to provide better safety. She climbed up past second bolt (clipped) and was in a precarious stance ready to clip third bolt. She took out a reasonable amount of slack then her foot slipped resulting in a fall. Fall was arrested just before she hit the ground and she narrowly missed the ledge underneath the climb. She was unharmed but I have injured my left hand. I had it gripped around the live rope to give the slack, she then fell and was caught by the rope which then became fully weighted at speed. This forced the rope out of my fingers which then whipped back again - causing trauma to the inside and outside of my left hand. This has resulted in soreness in all digits and bruising and swelling on the 3rd, 4th and 5th digits. Seems to be a soft tissue injury that will heal on its own with time.