MORPHOLOGICAL AND MOLECULAR EVIDENCE:
The vestigial structure in a whale is the pelvic bone. There are still studies being shown if the pelvic is actually necessary for the whales because they can still perform important roles in the body. Such as, pelvic bones can play a part in protecting sexual organs of the whales. The pelvic bones are argued to be as a vestigial part of the whale because they are there as hips and are too help walk but whales do not have the capability to do so.
"The evidence that whales descended from terrestrial mammals is here divided into nine independent parts: paleontological, morphological, molecular biological, vestigial, embryological, geochemical, paleoenvironmental, paleobiogeographical, and chronological" (http://www.talkorigins.org/features/whales/ ).
As stated before it is hard for evidence of whales to be found and is still being researched upon.