A composite yet monolithic, free abrasive grinding lap includes a sintered porous matrix of ceramic or metal material and a quantity of silicon, substantially completely filling the pores of the sintered porous matrix preform at least throughout an effective region of the lap that is to come in contact with a workpiece to be acted upon by the lap. The free abrasive grinding lap is made by first slip-casting a preform, then freezing and freeze-drying the same, followed by lightly sintering the dry preform into a porous matrix preform, bringing the temperature of the preform to above the melting point of silicon, and filling the pores with molten silicon.