A high-precision punch and die apparatus having a stationary frame (40); a punch (10) movable relative to the frame (40), the punch (10) including integral pneumostatic bearing surfaces (16, 18, 20, 22 et al.) and at least one cutting edge (14); and a die (26) adjustably mounted to the frame (40) to receive the punch (10) therethrough, the die (26) including at least one cutting edge (28a, b, c) coactable with the cutting edge(s) (14) on the punch (10). A pair of pneumostatic bearings (30 and 34) are provided to constrain and guide movement of the punch (10) through the die (26), each bearing (30, 34) having a segmented journal that includes a plurality of journal segments (30a, b, c, d and 34a, b, c, d) formed with a pneumostatic bearing surface (32a, b, c, d and 36a, b, c, d), the journal segments (30a, b, c, d and 34a, b, c, d) being adjustably mounted, relative to the frame (40), to receive the punch (10) therebetween so that the bearing surface (32a, b, c, d and 36a, b, c, d) on each journal segment (30a, b, c, d and 34a, b, c, d) is in closely spaced relation to an opposing one of the bearing surfaces (16, 18, 20, 22 et al.) on the punch (10). Also provided are means for controllably supplying a pressurized gas (G) to the bearing surface (32a, b, c, d and 36a, b, c, d) on each journal segment (30a, b, c, d and 34a, b, c, d), to facilitate constraining and guiding movement of the punch (10) through the die (26), and means (P) for effecting such movement of the punch (10) through the die (26) so as to move the cutting edge(s) (14) on the punch (10) into coacting relation with the cutting edge(s) (28a, b, c) on the die (26).