While Henman, 21, assumes the assurance and maturity of a man who has been at the top of his profession for decades, he refuses to be drawn into the trap of making promises which, he reasonably fears, he will be unable to fulfil.
"I don't think I'll be dancing in the street," the British No 1 concluded after needing just one game to beat Milligan after their match had been held over by rain from Friday with Henman poised to serve for the match at 6-1 6-3 5-4.
The contest was over in five points, 124 seconds, with Henman treating the Centre Court crowd to nine shots, to Milligan's six (not including the five-minute knock-up) on his way to a fourth-round meeting with the Swede Magnus Gustafsson and the chance of becoming the first Brit to reach the quarter-finals since Roger Taylor in 1973. That, agrees Henman, is a much more realistic aim than emulating Perry, even though the bottom no longer exists in the bottom half of the draw following the demise of Boris Becker, Andre Agassi and Jim Courier, with Todd Martin (13th) the only seed.
Henman's words have a rare air, in a British tennis player, of professionalism and ruthlessness. He added: "I'd never gone beyond the second round before so I'm obviously happy to be in the fourth round, but I still have to concentrate on what I'm doing.
"I was very close to the finishing line overnight, but I just had to make sure I came here and prepared as normal and did a professional job. I did nothing out of the ordinary; I practised, showered and prepared as if I was going to play a normal five-set match. Obviously it was one of the shorter days I've had on court. But that's very nice, thank you."
Milligan, a Tottenham fan who liked the club so much he turned down an invitation to join Arsenal as a 12-year-old, was just happy to play a part in the first Centre Court all-British clash for 58 years, before deciding whether to accept his invitation to a Wimbledon Ball. "The Who are playing in Hyde Park? Are they really? I might have to change my plans," he said.
No such distractions, unsurprisingly, for Henman, who chose to celebrate by going home for a kip before preparing for tomorrow's adventure: "I won't do anything out of the ordinary. I'll have a few hours' extra sleep, practise and relax."
If he beats Gustafsson and continues in this vein, it will be his last chance for a rest until he retires.