An attachment method and flange for connecting a ceramic matrix composite (CMC) component, such as a gas turbine shroud ring (36, 68), to a metal support structure. A CMC flange (20A) may be formed by attaching a wedge-shaped block (26) of a ceramic material to a CMC wall structure (22), and wrapping CMC layers (24) of the wall structure (22) at least partly around the block (26), forming the flange (20A) with an inner oblique face (34) and an outer face (35) normal to the wall structure. An adjacent support structure, such as a metal support ring (40A), may abut the outer face (35) of the CMC flange (20A) and be clamped or bolted to the CMC flange (20A).