The more recent research is showing that celiac testing is not necessarily accurate.
Tissue transglutaminase, TTG is released from damaged intestine during active celiac disease and the antibodies are found elevated in the blood of most patients with untreated celiac.
In order to have an accurate picture of celiac, you would be advised to feed your child gluten 2-3 times a day for 6 weeks before doing the test in order for a sufficient immune response to occur to be measured by the test.
And if your child is anemic, which is usually the case in untreated celiac, then the test will also not be accurate.
(This is true of many blood tests including A1C).
Another reason for a false negative is IgA deficiency, the most common immunodeficiency which affects 1 in 333 and occurs 10-15 times more frequently in those with celiac. (Immunoglobulin A (IgA) deficiency is 10 to 15 times more common in patients with celiac disease (CD) than in healthy subjects. http://cvi.asm.org/content/9/6/1295.full)
It is questionable if TTG testing is accurate at all in young children.
There are problems with antigliadin testing also. AG tests could be elevated in many other conditions also as well as in healthy individuals.
There are other signs of possible celiac for example, gastrointestinal, fecal fat, anemia, etc.
Even the intestinal biopsies are not reliable since celiac affected intestine might be for example farther down from where the samples were taken.
Also once you have been on a gluten free diet or even a low gluten diet, then all of the diagnostic tests are useless.
The only way to diagnose celiac via diagnostic testing is to gluten load. .
And for children who already feel better from a gluten free diet, how fair is it to intentionally make them sick, very sick just to try to get a positive diagnosis?