Which blood tests should I have to screen for celiac disease?

You should have both tTG-IgA and total serum IgA tests to screen for celiac disease. As long as you produce IgA (total serum IgA confirms you do), tTG-IgA is 98% accurate in measuring elevated antibodies. If IgA deficient, or if there is some other equivocating factor to potentially compromise the blood test, then an EMA blood test is also given.

Other gliadin antibody tests are not useful in screening for celiac disease.