Methods for extruding a ceramic-forming mixture through a honeycomb extrusion die (10), methods for forming a green honeycomb extrudate from a ceramic-forming mixture, methods of preparation of a honeycomb extrusion die (10) that extrudes a ceramic-forming mixture, and systems including a honeycomb extrusion die (10), ceramic-forming mixture, and abrasive flow media. The method of extruding a ceramic-forming mixture through a honeycomb extrusion die (10) includes conditioning the honeycomb extrusion die (10) by extruding an abrasive flow media through the slots (20) of the die (10) prior to extruding the ceramic-forming mixture through the slots (20) of the die (10). The abrasive flow media includes abrasive inorganic particles dispersed in a flowable carrier. The ceramic-forming mixture includes one or more types of inorganic ceramic-forming particles. The abrasive inorganic particles in the flowable carrier have a particle size distribution that corresponds to that of at least one type of the ceramic-forming particles in the ceramic-forming mixture.