A flat-panel display is hermetically sealed by a process in which a first plate structure (30) is positioned generally opposite a second plate structure (32) such that sealing material (34) provided over the second plate structure lies between the plate structures. In a gravitational sealing technique, the first plate structure is positioned vertically below the second plate structure. The sealing material is heated so that it moves vertically downward under gravitational influence to meet the first plate structure and seal the plate structures together. In a global-heating gap-jumping technique, the plate structures and sealing material are globally heated to cause the sealing material to jump a gap between the sealing material and the first plate structure. When the first plate structure is positioned vertically above the second plate structure, the sealing material moves vertically upward to meet the first plate structure and close the gap.