Some new friends I've begun spending time with recently are all religious people. Two or three times now, one of the girls has offered to pray before we eat. I have absolutely no idea how to handle that properly. I know I'm responsible for doing or saying something, but I don't know when or how.
I've run into it before, though it has been rarer of late. Somehow people expect a preacher to lead prayers in a gathering, so I usually end up being asked to lead a prayer.
There have been times when some woman announces that she is going to pray. When that happens, I don't participate. I'm respectfully silent, but I don't bow my head with the others. People pick up on that, and will sometimes ask. That becomes an opening to discuss I Timothy 2:11-12.
If a woman asks if I mind, I'll typically say "yes." I'm old enough now to realize that it is quite alright to speak my mind -- especially when I'm asked. How she responds to that then determines where I go from there.
When I don't participate in a prayer, I do say my own silently afterwards. Who knows, it might lead to a discussion about why.