A contact in Australia tells me she is descended through the mother line to Mary Jenison who married Robert Pymble. It would be interesting if there are others who have taken the test to prove a similar connection, or who may have thought to have the test.
A person's matrilineal or mothers-line ancestry can be traced using the DNA in his or her mitochondria, the mtDNA, as follows: This mtDNA is passed down by the mother unchanged, to all children. If a perfect match is found to another person's mtDNA test results one may find a common ancestor in the other relative's (matrilineal) "information table", similar to the patrilineal or Y-DNA testing.
However, because mtDNA mutations are very rare, a nearly perfect match is not as helpful as it is for the above patrilineal case -- in the matrilineal case it takes a perfect match to be very helpful.
Mitochondrial DNA (mtDNA) testing
Map of human migration out of Africa, according to Mitochondrial DNA. The numbers represent thousands of years before present time. The blue line represents the area covered in ice or tundra during the last great ice age. The North Pole is at the center. Africa, harboring the start of the migration, is at the top left and South America is at the far right.