How do they test for hemolysis?

Several labs. An elevated reticulocyte count or seeing numerous young red cells on a smear is a tipoff to hemorrhage or hemolysis in a patient. I recommend against haptoglobin or free hemoglobin tests. Coombs test picks up immune sensitization & there are a host of others. There are other situations, such as the blood bank, where other tests work.
Hemolysis. 1st is to repeat the test. 2nd is to look at a peripheral blood smear.