Her first delivery came with a vigorous flourish and produced a foot- tangling surprise. Instead of her racket being raised into the backscratcher position, as per coaching manual, it came down in a sideways parabola as though it were a sabre slicing a man off at the knees.
The effect upon a vulnerable young hopeful was similar. The ball curled over, lurched sideways, evaded by a considerable margin an adolescent effort to drive it back down the middle, and slithered into the tramlines like a sidewinder on a Namibian sand-dune.
Ace. The full-skirted lady was already turning to pick up the next ball. That brought a similarly wicked slice, a similar crazy break, and the same chastening outcome.
More prudent attempts to counter the underhand sorcery eventually enabled racket to be laid on ball, but rarely to be returned safely. Two aces in her first service game were followed by two more in the next, by returns which were cannon-fodder for her partner at the net in the game after that, and by regular wrong-footing humiliation throughout the match.
That was how I lost to Henman's granny.
Extremely discreet enquiries revealed that the lady's ladle had made fools of better and more experienced men than I. Indeed, on a windy day at Lee-on-Solent Susan Billington had apparently been known to serve four swirling aces in one game.
Nice to imagine that her glint, the composure and the cleverly masked skill have found expression again, almost 40 years later, in Britain's best hope since Fred Perry. But perhaps the obstinate individualism of the long-flannelled partner at the net had a more obvious influence upon the Henman dynasty.
Henry Billington, ruddy-faced and Wiltshire-vowelled, competed at Wimbledon and in the Davis Cup, and his record of playing at county week from 1927 to 1961 shows how much he enjoyed local tennis even while still an international- standard player.
It was one of the reasons why he and his wife, still formidable in the late 1950s even though both were aged in their late 40s, occasionally unleashed themselves on such unsuspecting county juniors as myself.
Mixed doubles and other events in seaside tournaments provided the remarkable couple with friends, fun and - in the later stages at least - useful competition as well. They had a holiday home on the Hampshire coast which they and their children, Tim, Tony and Jane, used as a base for six or seven different tournaments. For them it was a perfect arrangement, but for unknowing local players it sometimes brought nasty shocks.
Billington was a farmer's son who learned to play in the garden, developing an idiosyncratically effective style in which he hit the ball with the same side of the racket on both backhand and forehand and with limited spin while serving. He had a healthy contempt for coaching.
Billington believed players with orthodox styles were easier to read, and it was a source of amusement when he reserved his most obdurate performances for those occasions when he met the most obviously coached players.
But though Henry's style was all his own, Susan's was not. It may have been apocryphal that she was advised by her mother Ellen Stawell-Brown (one of the first women to serve overarm at Wimbledon, though not the first as sometimes reported) to serve underarm because she thought the other method rather strenuous for women. What is certain is that Henry persuaded Susan to use it when they played mixed doubles together.
Susan served overarm perfectly well when playing with the children. But Henry believed the underarm service sat down so low, and caused opponents to hit up so much, that it would create more chances for him to march across the net and thump clumsy returns away. Repeated experiments proved him correct and Susan became the last player regularly to serve underarm at Wimbledon.
Henry's homespun style and attitudes remained surprisingly effective long after the war, even when the "American twist" serve, and players with varieties of spin on both wings became more commonplace. Father's enduring excellence thus influenced the children, but becoming a high- class, self-taught player before the war was quite different from trying to learn through competition in the 1950s, and this influence became a mixed blessing.
Tim Billington, the eldest child, was a good county player but did long not harbour serious ambitions in tennis, and the second son, Tony Billington, had plenty of ability though not quite the technique necessary to do really well as top-level standards rose sharply.
Jane, Tim Henman's mother, had fine flowing groundstrokes and played for both Berkshire and Oxfordshire. But she gave up regular tournament play in her early twenties after getting married and was not able, as some reports suggested, to compete at senior Wimbledon.
Tony, an Oxford blue who played in the Wimbledon qualifying competition, was the nearest to making it - but never quite did. "This was a pity: had I done so four generations of the family would have played at Wimbledon," he said. All three children became highly successful in other areas of life, but in tennis terms the fullest expression of the dynasty's talents skipped a generation.
Today Henman travels with his own coach. This has less to do with any reaction against the Henry Billington philosophy, and is more an indication of how much the professional era has changed tennis. Perhaps, though, in the choice of the British champion's coach there is a hint of family legacy.
Continuity, loyalty and trust have become highly regarded values among the Henmans, with the influence of such a long-lasting family tennis tradition (father Tony Henman was a useful player, too). Tim Henman's coach, David Felgate, in addition to being a former player and knowledgeable in his role, is a respected family friend.
"For me it's like having a younger brother to help," Felgate says. He has observed the building up of Henman's once-skinny frame into a wirily strong body, his legs strengthened significantly in the past two years. The past 12 months have seen a good all-round international player develop into a dangerous top-level competitor with the emergence of one genuinely potent weapon.
This is Henman's forcing first serve, which he can unleash on the important points, and which provided just the improvement he had needed to project himself into the top 20. Henry Billington, sceptical of technical changes or not, would have been impressed.
Certainly Susan Billington is. She stopped playing only six years ago, at the age of 80. Now the exciting rise of her celebrated grandson has provided a wonderful new interest at a time when she has needed it.
Susan expects to be watching at Wimbledon this year. Quite likely she will observe, shrewdly, Henman's attempts to find the best selections of the various tactical options which improvement has made available to him.
He can serve, rally, and time his approach; serve, drive and volley; serve and volley; serve and slug out a clay court-type rally from the back. All can be combined in different ways at different times. "The trick is to become more aware of when the ball is there to be hit and when it isn't", Felgate says.
I shall try to cast a glance in the direction of grandma while Henman is attempting it. I hope it gives her satisfaction. She certainly knew - but kept it secret, of course - plenty about all this. With or without a coach.