Britain will now face the so-far unstoppable Canadian side who are the hot favourites for gold and topped the round-robin standings with nine victories from as many matches.
Leading 7-4 going into the final end against Denmark, Muirhead and co somehow conspired to throw the match away and lost 8-7 in the extra end.
The defeat means they were leapfrogged into third place by Switzerland who beat China 10-6 in the evening session.
Switzerland will therefore face Sweden in the other semi-final after the Swedes completed the round-robin action with an 8-4 win over Japan for a record of seven wins from their nine matches.
- Sports & Recreation