A method of making a vacuum insulating glass window unit comprising first and second glass substrates (2, 3), each said substrate having first and second major surfaces, the method comprising: applying a first lead-free frit material (15a-d) around perimeter edges of the first major surfaces of the first and second substrates (2, 3); heat treating the first and second substrates (2, 3) with the first frit material (15a-d) thereon, the first and second substrates (2, 3) reaching a first peak temperature; following said heat treatment, applying a second lead-free frit material (17a-b) on the first and/or second substrate(s) (2, 3) such that, for each substrate on which the second frit material (17a-b) is applied, the second frit material (17a-b) at least partially overlaps the first frit material (15a-d) on the respective substrate around peripheral edges thereof, the first and second frit materials (15a-d, 17a-b) having different compositions; positioning a plurality of spacers on the first surface of the first substrate; bringing together the first and second substrates (2, 3) such that the first major surfaces of the first and second substrates (2, 3) face one another, and such that a cavity is defined therebetween, in making a VIG unit subassembly; heating the subassembly in order to melt the second frit material (17a-b) and wet the first frit material (15a-d), the heating being performed such that the first and second substrates (2, 3) reach a second peak temperature that is no higher than 400 degrees C and that is at least 150 degrees C lower than the first peak temperature; following said heating of the subassembly, cooling and/or allowing the subassembly to cool, in forming an edge seal between the first and second substrates (2, 3); evacuating the cavity to a pressure less than atmospheric via a pump-out port; wherein the pump-out port is a pump-out tube provided in a hole drilled in one of the first and second substrates; and the method further comprising applying - the first frit material (15a-d) to interior surfaces of the hole and/or to the pump-out tube prior to said heat treating; and - the second frit material (17a-b) as an outermost frit material around the pump-out tube prior to said heating of the subassembly; and sealing the pump-out port in making the VIG unit. applying a first lead-free frit material (15a-d) around perimeter edges of the first major surfaces of the first and second substrates (2, 3); heat treating the first and second substrates (2, 3) with the first frit material (15a-d) thereon, the first and second substrates (2, 3) reaching a first peak temperature; following said heat treatment, applying a second lead-free frit material (17a-b) on the first and/or second substrate(s) (2, 3) such that, for each substrate on which the second frit material (17a-b) is applied, the second frit material (17a-b) at least partially overlaps the first frit material (15a-d) on the respective substrate around peripheral edges thereof, the first and second frit materials (15a-d, 17a-b) having different compositions; positioning a plurality of spacers on the first surface of the first substrate; bringing together the first and second substrates (2, 3) such that the first major surfaces of the first and second substrates (2, 3) face one another, and such that a cavity is defined therebetween, in making a VIG unit subassembly; heating the subassembly in order to melt the second frit material (17a-b) and wet the first frit material (15a-d), the heating being performed such that the first and second substrates (2, 3) reach a second peak temperature that is no higher than 400 degrees C and that is at least 150 degrees C lower than the first peak temperature; following said heating of the subassembly, cooling and/or allowing the subassembly to cool, in forming an edge seal between the first and second substrates (2, 3); evacuating the cavity to a pressure less than atmospheric via a pump-out port; wherein the pump-out port is a pump-out tube provided in a hole drilled in one of the first and second substrates; and the method further comprising applying - the first frit material (15a-d) to interior surfaces of the hole and/or to the pump-out tube prior to said heat treating; and - the second frit material (17a-b) as an outermost frit material around the pump-out tube prior to said heating of the subassembly; and - the first frit material (15a-d) to interior surfaces of the hole and/or to the pump-out tube prior to said heat treating; and - the second frit material (17a-b) as an outermost frit material around the pump-out tube prior to said heating of the subassembly; and sealing the pump-out port in making the VIG unit.