Four times: 1998: lost to Pete Sampras in four sets.
1999: lost to Pete Sampras in four sets.
2001: lost to Goran Ivanisevic in five sets.
2002: lost to Lleyton Hewett in three sets. Each player that defeated Henman in the semis won the Championship in their next match.
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never. He got semi finals 4 times though :
1998: lost to Pete Sampras in four sets.
1999: lost to Pete Sampras in four sets.
2001: lost to Goran Ivanisevic in five sets.
2002: lost to Lleyton Hewett in three sets.