A ceramic filter has a structure that comprises first and second surfaces and an arrangement of flared passageways wherein the flared passageways extend between and connect with said first and second surfaces. The flared passages may be generally circular and more than 90% can have a diameter greater than 0.1μm. An opening of the passages may have a diameter of less than 50μm. A blood filtration apparatus may incorporate the ceramic filter and may advantageously find use in membrane filtration for the industrial separation of blood cells to eliminate leukocytes (to reduce the risk of infection).