You don’t want the extra responsibility, do you? So:
1. Assume that your work speaks for itself. Don’t bother to keep a record of your contributions to the organization. Rely on your (busy) boss to remember everything you’ve done, and understand why it’s significant. Keep believing that, if you “deserve” it, you’ll surely get it.
2. Focus on your experience to the exclusion of your potential. Keep reiterating the past so that you’re seen as an indispensable go-to person for what you’ve already done, rather than as the powerful choice for bigger things.
3. Doubt yourself. Because it’s so much more appropriate, and productive, to offer up false humility to the men.