The circular waveguide transition consists of a tapered length of waveguide with flanged ends, manufactured by casting an aluminium alloy into a sand mould. The mould consists of two identical halves each with the imprint of the outer dimensions of the tapering waveguide and the outer dimensions of two rectangular housings (12, 13) each containing a negative mould for the flange. A tapered core (3, 11) of the same dimensions as the inner dimensions of the tapering guide joins the two housings. The gap between core and mould is connected to the flange moulds inside the housings. After the casting has solidified, the core is removed by thermal shock.