But how? If he tried to raise her arm, he might lift her off the floor. In the event, he opted for a pre-emptive strike.
As Mrs Shephard walked from the platform to the blue circle where she was to deliver her speech, Mr Major popped out from behind a screen, gave her a kiss and sat down to listen.
She responded by saying he could have more grammar schools - if parents wanted them. "Prime Minister, we may even see a grammar school in every town," she twinkled at him, making it clear that she did not particularly want them.
During much of the speech, Mr Major might have been forgiven for dozing off. Although Mrs Shephard had plenty to announce - and did not, for once, have to leave the most interesting news to the Prime Minister - her style and delivery were competent rather than spell-binding. She is a politician far better suited to the informality of the fringe meetings she charmed all week than to the big conference set-piece.
However, a speech in which she stressed the themes of choice and diversity, with a strong section on discipline and some ridicule for Labour politicians, rang enough bells with her audience to win her a standing ovation.
The Education and Employment Secretary announced: * measures in the forthcoming Education Bill to encourage selection, including giving the Funding Agency for Schools the power to set up new grammar schools; * extending the Assisted Places Scheme to private schools for 5 to 11-year-olds;
* a national curriculum for initial teacher training to teach all new teachers "the methods that really work for reading, writing and arithmetic" (this won the loudest applause of the speech);
* a crackdown on disruptive pupils, with a longer exclusion period, admission to schools dependent on parents signing home-school agreements and the return of detention;
* a December White Paper on 14 to 19-year-olds that will set out ways of strengthening post-16 qualifications and introduce learning credits to help young people choose what and where to study.
Mrs Shephard was replying to a debate in which one prospective parliamentary candidate after another deplored Labour's plans to abolish the Assisted Places Scheme and highlighted the Labour threat to grammar schools.
"Tony Blair says Labour has no vendetta against grammar schools and that their future is a matter for local people," Stephan Shakespeare, prospective candidate for Colchester, said. But their future would be decided by a "sour grapes ballot" in which Labour would be able to draw the boundaries of the electorate.
The next day, the Prime Minister began his conference address on opportunity and choice with the subject of education. Stressing that each child was unique and should not be made to fit into a regimented education system, he said the Government's task was "to provide a rich choice of schools and colleges".
"Who should choose the right schools for those children?" he asked. "The Government, the bureaucrats in Whitehall, the councillor in the town hall or the parents who love and care for those children? Of course, the parents. "
And he made it clear, perhaps in response to Mrs Shephard's remark the day before, that parents and not central government would drive the move back to selection.
"If parents want more grant-maintained schools, they shall have them," he said. "More specialist schools, we shall provide them; more selection, they'll have it. Why should Government say no, if parents say yes? And if parents want grammar schools in every town, well then so do I and they shall have them. "
Mr Major also announced the establishment of a committee chaired by the England cricketer, Sir Colin Cowdrey, to oversee a programme under which leading sportsmen would visit schools to instil in pupils a love of sport.
"I want them [pupils] to enjoy sport and they will enjoy it more if they play to win," he said. "Take it from me - winning is fun."