Standard solderless connectors extend from a molded package body supporting at least one high power LED. The package includes a relatively large metal slug extending completely through the package. The LED is mounted over the top surface of the metal slug with an electrically insulating ceramic submount in-between the LED and metal slug. Electrodes on the submount are connected to the package connectors. Solderless clamping means, such as screw openings, are provided on the package for firmly clamping the package on a thermally conductive mounting board. The slug in the package thermally contacts the board to sink heat away from the LED. Fiducial structures (e,g., holes) in the package precisely position the package on corresponding fiducial structures on the board. Other packages are described that do not use a molded body.