Clijsters, the number one seed and world number one, eased past Slovenian qualifier Tina Pisnik 6-3, 6-2 while second seed Henin, number two in the world, marched through with a 6-4, 6-2 victory over Russian Vera Zvonareva.
"It is one of the best matches I have played since the U.S. Open," said Henin, who beat Clijsters in the Flushing Meadow final in September and at the French Open final.
"She (Zvonareva) always played really well, she is very solid and she is young so she has nothing to lose. I had to play a good match and I did."
Henin, who also announced she was pulling out of next week's Linz tournament in Austria to rest, will face Russian Nadia Petrova in the semis after the world number 14 comfortably overturned her compatriot Elena Bovina 6-1, 6-4.
Clijsters faces a tough test against world number 25 Jelena Dokic after the Yugoslav put out defending champion Patty Schnyder of Switzerland 6-0, 6-3.
Henin-Hardenne got the crucial break at 3-3 at the fourth attempt in the first set of her match with seventh seed Zvonareva. The Belgian then saved a break point on her own serve when 5-4 up before going on to claim the set.
She broke Zvonareva twice in the second set before the Russian saved two match points when 5-1 down to keep the game alive. But Henin-Hardenne eventually sealed the win after missing out on another match point on serve.
NEAR PERFECT
Clijsters was near perfect on serve in the opening set of her match with Pisnik, losing just three points, and completed it with her fifth consecutive love game after missing her first set point at 5-2.
After a series of breaks of serve at the start of the second set, Clijsters broke for 3-2 in the fifth and then crucially held serve to love in the sixth.
She sealed her second break to go 5-2 up and comfortably served out to complete victory in just 54 minutes.
"I have had some tough matches against her in the past so I tried to do something a little bit different," said Clijsters.
A resurgent Dokic, who had not won consecutive matches in 10 tournaments before arriving in Zurich, put in a blistering performance, losing just 10 points and breaking Schnyder three times to win the first set in just 17 minutes.
She had moved to 3-0 with another break in the second before Schnyder finally secured her first game. The crowd came alive as she continued to hold serve but it was not enough to stop Dokic winning comfortably in 48 minutes.
