It is common sense that you should never introduce a woman to a man, but there is one exception: when you introduce an elderly gentleman (or an important one) to a younger lady, the rule is reversed, and so the woman will be introduced before.
This attitude of respect, however, could not be too pleasing to the man who, if he still feels himself young, will be irreparably offended. It will be up to your sensibility to understand with whom you are dealing. If it happened to my grandfather, it would be a disaster, you know… 98 years old and still going strong! Long life to the grandparents who still feel the Saturday night fever and want to be gentlemen at all ages!