Grandparentage testing can be useful for establishing a relationship in situations where the potential father cannot be tested. It can be used to examine the relationship between a child and a possible grandparent, although the inclusion of other close relatives in the test is always recommended.
Grandparentage testing can be used to establish the paternity of a child when samples can be obtained from both paternal grandparents (should you wish to identify a maternal relationship then both maternal grandparents will be required to provide samaples). If the mother and only one of the paternal grandparents are available, the test will provide a strong indication of whether the two individuals are related but it cannot provide a conclusive result.
It is possible to just compare the DNA profile of a child and an alleged grandparent (although we prefer that the mother is tested). This can provide an indication of a relationship but, because of the patterns of DNA inheritance, it will not always reveal the true nature of the relationship. Such an analysis can only report the most likely relationship given the DNA evidence.