The urine dipstick has a bunch of squares, each with a chemical analysis ready to go. The dip will semiquantitatively show you what is in the urine. My bet would be hemoglobin but various urine dipsticks will have various substances on there. A dipstick will detect hemoglobin which will come out of any blood cells once they lyse on sitting in storage for a while. Free hemoglobin can be in fresh urine too if a person is hemolyzing. Another brown thing could be bilirubin. All detectable with chemistry.
A serum chemistry lab will quantify many different things in serum - again bilirubin would be my bet as a common component of serum. You can look for almost anything and a clinical lab can run a chemistry test to determine presence or quantity of that thing.
Chemistry tests could miss nonchemical microscopic brown things. Bacteria or mold could contaminate your specimens, or there might still be red blood cells present. You could look for these things under a microscope.