A system for making cell blocks includes a cell block cassette and processing station, the cassette including a main body having a having a collection aperture formed therein and a filter assembly removably attached to the main body, the filter assembly defining a collection well in communication with the collection aperture, and having a filter positioned across a bottom surface of the collection well, the filter configured to retain cellular matter carried in a fluid that is dispensed into the collection well and flows across the filter. The cell block processor has a cassette interface removably seating the cell block cassette, and a sensor positioned or positionable to detect and monitor a fluid level in the collection well. The processing station includes an automated fluid delivery system operable to dispense a fluid into the collection well, and a controller operatively coupled to the fluid delivery system, wherein the controller causes the fluid delivery system to selectively dispense fluids into the collection well based at least in part on a flow rate across the filter determined at least in part based on changes in the monitored fluid level in the collection well.