About 70 to 80% of celiacs test positive on the blood and biopsy exams. I had the Quest panel - it showed an elevated anti gliadin antibody, the anti tissue transglutaminase was not elevated and I had an allergy to cows milk. The low anti ttg could have been negative because I had sprue and most or all of my villi were flattened. But this confused the DR so I immediately ordered a DNA marker test from Enterolab.com. This test showed I carried a main celiac gene (HLA DQ allele b 0302 or a DQ8) and a gene which predisposes to Leaky Gut Syndrome/non-celiac sprue (allele b 602 or a DQ6). The Quest test may now include a test for endomysial antibodies, another bit of evidence.
There is a serology test for CD which defines the shape of the necessary antigen recptor which some Drs find more helpful than the genetic tests. (see Prometheus Labs). Enterolab also offers tests for the autoimmune antibodies which are more sensitive for the auto antibodies, other food allergies and fecal fat.
There are a very few people who test negative for CD but have the symptoms and improve on a gf diet. Some post on Celiac.com Forums.