There is disclosed a contact pin assembly for a high voltage electrical connection, the contact pin assembly comprising: an electrically-conductive outer member which is supportable from a support member, the outer member having a bore extending therethrough, the bore defining a smooth inner face of the outer member and being divergent towards opposite ends of the outer member; a contact pin, ends of which are arranged to be connected directly or indirectly to cables, the contact pin extending through the bore and having a profiled portion which defines a smooth outer face of the contact pin and which is divergent towards opposite ends of the contact pin, the contact pin being concentric with the bore; an electrically-conductive layer provided adjacent the inner face, the electrically-conductive layer being in electrical communication with the outer member and conforming with the profile of the inner face; an annular space between the profiled portion and the electrically-conductive layer; electrical insulation surrounding the pin to provide a seal around the pin and filling the annular space; and sealing between the insulation and the ends of the outer member. There is also disclosed a method of manufacturing such a contact pin assembly.