The invention relates to a method of manufacturing a semiconductor device whereby an upper side of a wafer of semiconductor material (12) is provided with semiconductor elements in passivated mesa structures (2), which semiconductor elements are provided each with a connection electrode (7') in that according to the invention conductive contact bodies (3') are provided on upper sides (7) of the mesa structures (2), and an insulating material (18) is provided in spaces (17) between the contact bodies, whereupon the wafer (1) is split up into individual semiconductor bodies (10) which comprise passivated mesa structures (2) and contact bodies (3') surrounded by insulation. The contact bodies (3') have dimensions such that the semiconductor bodies (10) are suitable for surface mounting. The semiconductor devices made by the method according to the invention are resistant to comparatively high voltages between the connection electrodes (7', 4). The method has the additional advantage that the semiconductor device can be readily manufactured in certain standard dimensions such as exist for SMDs through adaptation of the dimensions of the contact body (3').