Previous reports of ultrafast laser welding of glass-to-glass have indicated that a pre-existing optical contact (or very close to) between the parts to be joined is essential. In this paper, the capability of picosecond laser welding to bridge micron-scale gaps is investigated, and successful welding, without cracking, of two glasses with a pre-existing gap of 3 µm is demonstrated. It is shown that the maximum gap that can be welded is not significantly affected by welding speeds, but is strongly dependent on the laser power and focal position relative to the interface between the materials. Five distinct types of material modification were observed over a range of different powers and surface separations, and a mechanism is proposed to explain the observations.