Use a jeweler's saw to cut wire coils into chain maille jump rings.
If a power saw cutting tool isn't available good results can achieved by using a jeweler's saw.
Smooth even precise cuts can be made which will allow the jump rings to be opened and closed correctly.
Two of the methods that can be used are the wrapped coil approach and the use of a wooden dowel inside the wire coil.
These techniques require a jeweler's saw, masking tape, wooden dowel and a small vice.