Darren,
The answer is, It depends...
How steep is the taper? Is it one side only or is it symmetrical? Is it a flat tapered piece or is it a round tapered piece? These will play into the correct answer for your situation.
Most old toolmakers have a drawer in their tool chest filled with taper grabbers that look like a chordal piece cut off of a round disk. (We almost always cut off the sharp pointy ends to make life less bloody.) The flat side goes against the part and the round side goes against the vise jaw such that it will pivot to provide pressure to the part. If the taper is symmetrical, we swing the vise to half the included taper angle.
If the part is round, we mill a vee in the (flat) contacting surface and mount a flat v-block on the fixed jaw of the vise. It becomes a lot more complicated as the vee itself will affect the angle of the part being held and the calculated solution to that is far from simple. A good test indicator with a depth stop on operations coupled with a lot of tapping the angle about the swivel base of the vise (accompanied with an appropriate amount of swearing) is usually faster and accurate to the accuracy of the indicator.
There are also self-centering 4-bar mechanism tools that will do this job. A piece of the old cloth-type of electrician's tape is often placed against the moveable jaw of the vise to improve friction between the vise and the taper grabber.
Another variation you will see is a plate with four dowel pins pressed into it. The two outboard dowel pins get an eccentric collar oriented such that the force of the cutter increases the locking of the part into the trap. A variation on this is to have a step milled along one face (fixed jaw side) that only uses two (outboard -- moveable jaw side) dowel pins. I have even seen (and I believe they used to be commercially available, I have never owned one) vises where the moveable jaw was set to pivot.
Does this help you skin your cat?
