Mel: I'm one that doesn't personally see this as just a gender issue...it's an issue to anyone that has a heart. By many standards it's a sign of weakness, but people with compassion often have leadership abilities that hard hearted folks can't replicate.
I have had employees - male and female - cry in my presence...and I handed them to tissue box and let them get it out of their system. But, I am not uncomfortable with tears - whether male or female...clearly these other guys are...
Crying is an emotion. Anger is too. If someone gets angry in a meeting and goes ballistic, it's as difficult to handle as someone being inconsolable. Crying may be seen as a weakness, but so is the inability to control a bad temper...and with the temper usually comes legal liability to a lot of "stuff"
Don't be afraid of tearing up, but don't allow yourself to be in a position of becoming inconsolable...get up, take a break and reach deep within for the resolve to clearly and constructively articulate what needs to be said. You might be surprised at how strongly and articulately you convey your point. Having a written outline of thoughts to fall back on can be very helpful in keeping your composure as well.
As to the "moral support" - go for it. No explanation is needed except that "XX is familiar with the situation, has valuable perspective, and can add moral support and depth to the discussion..."
If you don't grow where you're planted, you'll never BLOOM - Will Rogers