As far as i know there is no many test for Cpn for commercial use. In my country, and i think everywhere, there is only ELISA blood test fot Cpn.
This test finds only antibodies of three types - IgA, IgM and IgG. I'm not sure but thing that IgG is for old infection, IgM is for accute one, and not sure about IgA. So the others may more accurately explain you for the antibodies and the false negative results, but as i know the Cpn bacteria has three phases of development and the blood test can not detect the infection in all phases off.
Anyway, if you have possitive ELISA test you must be sure that you have chlamydia and must take measures.