The active infection tests are probably as good as they can be, and that is "not very good". They can detect the presence of the virus RNA, but are plagued by false negatives. This is not because the test is faulty. It's because there was little RNA where they swabbed. Rectal swabs would probably work a lot better, but nobody wants to do that! (Medical people AND patients.) They also can return positive results when all the active virus is gone and the patient is shedding old virus RNA fragments. To make a test that can tell the difference would require live cell cultures and cost thousands of dollars per test.

The antibody tests suck as well, not because of the tests (assuming a good brand) but because so many recovered victims do not make a lot of IgG antibodies. The full adaptive immune response takes a while and apparently lots of people clear the virus before the B-cells start making those antibodies. It does not mean they are not immune: There are memory B-cells that might know how to make antibodies, but never really got stimulated. We don't know and we don't know how long they will remain active.