Henin-Hardenne and Clijsters met in two all-Belgian Grand Slam finals last season, with Henin-Hardenne winning in the French and US Opens.
With No. 3 Venus Williams out in the third round, Serena Williams not defending the title and No. 4 Amelie Mauresmo forced to default her quarterfinal because of a back problem, Clijsters and Henin-Hardenne were strong favorites for the title.
Clijsters said her ankle wasn't as painful as it was when she withdrew from a warmup tournament in Sydney. She said she "just sort of jammed it again."
She started with only three unforced errors as she raced for a 5-0 lead in the first set, but ended with 47 unforced errors to Myskina's 45.
"I started off really well, was feeling good ... I wish I ended like that," Clijsters said. "I had a little stumble in the second, then I got taped very tight, which kept me from making it any worse. That's maybe why I was rushing it a bit.
"I was very happy I could pull it off in two sets, otherwise it would have been hard."
Schnyder described her run to the semifinals as "enormous."
"I mean, I'm so happy to be here and to play semis ... it's hard to describe," said Schnyder, who beat 12th-seeded Paulo Suarez in the third round and Nathalie Dechy in the fourth.
Raymond, a third-round winner over Venus Williams, is 0-5 in her career against Schnyder. The 30-year-old American had 44 unforced errors and only 24 winners.
"I don't think that I've been this disappointed losing a match," Raymond said. "I really, really thought that I had a good shot of really having a breakthrough here.
Raymond's loss leaves Agassi as the only American still in contention at Melbourne Park.
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