But at the age of 25 the harsh truth is that he is unlikely to improve any further. If a player is to become a regular winner of Grand Slams titles and a contender for the world number one spot, they have usually made the breakthrough by now.
British fans are now wondering when that day will come. Most commentators believe he has the potential to claim the biggest prize in tennis.
He can play every shot in the book and his desire to win and mental strength are top class.
But at the age of 25 the harsh truth is that he is unlikely to improve any further. If a player is to become a regular winner of Grand Slams titles and a contender for the world number one spot, they have usually made the breakthrough by now.
Pat Rafter was 24, Andre Agassi 22 and Sampras just 19 when they picked up their first major titles.
Now Henman finds himself anxiously looking over his shoulder at the likes of Lleyton Hewitt, 19, Tommy Haas, 22, and Nicolas Kiefer, also 22.
Highs and lows
That said, Henman's recent record at Wimbledon is second only to Sampras himself. He has reached the semi-finals for the last two years, losing both times to the six-times winner. The two years before that Henman reached the last eight.
The most worrying aspect of his game for British fans is that in the last year or two he has followed a great win by losing a match he should have won.
One week he can beat Yevgeny Kafelnikov or Andre Agassi and the lose to the likes of Jerome Golmard, Rainer Schuttler or Guillermo Canas.
Golmard is a particular bogeyman for Henman. He does not have a fraction of the British player's talent yet beat him twice last year.
There was a prime example of this in Rotterdam in February when Henman reached the final after beating Kafelnikov, the world number two at the time.
But just when fans thought he was about to secure his fifth career title, he lost to the 31-year-old Frenchman Cedric Pioline, ranked 51. That was Henman's sixth successive defeat in a final.
A few weeks later in Florida he squandered four match points against Agassi.
But hang on....
Keep it in perspective, though. If, five years ago, British tennis fans were told they would soon have a genuinely world class player who regularly beat the top names and always reached the final stages of Wimbledon they would have grabbed it with both hands.
The fact that the final step has so far eluded him may be frustrating but it is testament to the increased expectation of fans and the enormous talent of Henman himself.