Noel,
I will tell you 2 ways that will give different results.
The HAND JOB
is the least damaging to edges of ports but does not remove much material. This is the BEST way when re-ringing or trying to remove minor scuffs.
* Using a small 2 inch by 4 inch piece of 600 grit wet dry paper (Used wet) go back and forth around the bore in all areas the ring rides making a slight cross hatch pattern.
Be careful working on the area of scratches making sure you DON'T sand threw the chrome. You WILL NOT be able to remove all the damage, only clean up the burr that is at the top edge of the scratch.
Second is a specialty hone that is known as a FLEXHONE and is manufactured to a specific bore size that keep the little balls in light contact with surface of bore.
These type hones do a FANTASTIC job of evenly honing the bore into a cross hatch pattern taking any high spot away in the process.
They use 320 grit silica carbide balls that are VERY abrasive, so care with minimal time is bore needs to be maintained.
Picture below.