"In simple man's terms," he said, "there are two things that are going to happen: I'm either going to win, or I'm going to lose."
Henman was in a similar position a year ago, playing Sampras in the semi-finals. In simple man's terms, Henman's confidence has grown with experience, and so has the weight of expectation. His opponent has shown signs of wear and tear during the past 12 months, but is not lacking motivation.
Sampras may not last for ever, but the American is perfectly capable of winning two matches that will reward him with a sixth Wimbledon title, one more than Bjorn Borg, and a 12th Grand Slam singles title, equalling Roy Emerson's record.
The winner of the Sampras-Henman semi-final will play either the No 4 seed, Andre Agassi, the 1992 champion, or the No 2 seed, Australia's Pat Rafter, the US Open champion for the past two years.
Sampras, having won his previous five matches against Henman, from a concrete court in Tokyo in 1994 to the lawns of London's Queen's Club less than three weeks ago and with two victories at Wimbledon along the way, hardly needs a refresher course in how to approach the task. Some observers may also raise the point that Sampras's friendship with Henman also gives the American a psychological edge, although both players would scoff at the suggestion.
"We get on pretty well," Henman said. "We've got similar interests, we've got a fairly similar profession, and it means we see each other quite often. But it's as simple as that. We've practised quite a lot together. He knows the way I'm going to play, and I know the way he's going to play. There will be opportunities, and it's who takes them on the day."
That is the crux. Henman, the No 6 seed, whose fortitude saw him through an epic fourth-round contest against Jim Courier, cannot afford to be as profligate with his chances he was on the way to winning yesterday's quarter-final against Cedric Pioline, 6-4, 6-2, 4-6, 6-3.
Henman created 18 break points and converted four of them. That was enough to see off Pioline. But, as the Frenchman knows from the painful experience of losing to Sampras in both the 1997 Wimbledon final and the 1992 US Open final, if the world No 1 gives you even the sniff of a chance, you pounce, or pay the price.
"If you want to be critical," Henman said, "then you'd have to say that you'd want that ratio [of break points converted] to be a bit higher. But once I got my chances in the three sets I won, there was no way I was going to let them go."
The sun shone brightly on Henman and his supporters, in marvellous contrast to Thursday afternoon when he and Pioline were able to complete on Court No 1 for eight minutes before being rained off. Yesterday, Court No 1 was transformed from Dimbledon to Timbledon.
One point soon became apparent when the match resumed: Henman was hungrier for success than his opponent, who had lost his serve on his way back to the grounds. Pioline had lamented that he had mislaid it earlier, during the course of his fourth-round win against the Slovak Karol Kucera.
Seventeen double-faults contributed to Pioline's downfall - the first having been donated to Henman on Thursday, before play has been suspended after Henman had held serve to 15 and had taken Pioline to a couple of deuces - and the statistic looked even more woeful when set against Henman's 19 aces.
French colleagues describe Pioline as a chambrer (teasing) character, and he lived up to his reputation yesterday. First, his serve went, then his right knee seemed about to follow it. Having lost the first two sets, and forced Henman to save a break point with an ace at the start of the third set, the Frenchman called for the trainer and took a time-out for treatment.
The knee was massaged, and Pioline strode out to serve, somewhat renewed in spirit. "What concerned me," Henman said, "was that he had been serving quite a few double-faults, and his next second serve was 119mph in the corner. I had a slight question about what sort of cream went on his knee."
Pioline said that the knee did not trouble him as much as the loss of his serve. He broke for 2-1 and managed to save four break points in the concluding game to reduce Henman's lead to two sets to one.
The Briton double-faulted at 40-15 in the opening game of the fourth set, at which point Pioline heard rock music from a truck passing the grounds, and decided to dance. The crowd was more amused than his opponent. "I never really knew what to expect from him," Henman said. "I was trying to remain upbeat. I don't think he was suffering from nerves out there."
Henman, who finished the job in only 28 minutes, will need to be upbeat when he plays The Master today. He know what he is up against. "My game has come a long way," Henman said. "I feel much more consistent overall, and I think having played in a semi-final before is a very good experience. I'm just going to go out there and continue with the way I've been playing, and I don't feel like I've got anything to lose.
"He's played 45 Wimbledon matches in the last seven years, and he's won 44 of them. That record is self-explanatory."
Asked if he believed in underdogs, Henman responded: "Sure. Underdogs have won on plenty of occasions in plenty of different sports. I hope I can prove that again."
He can, too, given the right shots, the right attitude, and the right backing from a packed Centre Court... weather permitting.
Agassi ready to raise his game again, page 30