A mask (110; see also 160, 210, 260, 310, 408, 500, 702, 802, 904) having a plurality of openings (cells) is disposed on, or nearly on, the surface of a substrate (102), the openings (112) of the mask being aligned over a corresponding plurality of pads (104) on the substrate. The openings in the mask are filled with solder material (114). A pressure plate (120) is disposed over the mask to capture the solder material in the cells. Heat is directed at the mask (through the pressure plate) to reflow the solder. This is done in an inverted or partially inverted orientation. The stackup (assembly) of substrate/mask/pressure plate may be un-inverted prior to cooling. Mask configurations, methods of mounting the masks, and solder material compositions are described. The methods are robust, and are well suited to fine pitch as well as coarse pitch ball bumping of substrates.