I simply sit in silence without bowing my head. I taught my children that we should respect other people's rights to hold their beliefs, but we don't have to respect the beliefs themselves. Let the children decide whether to bow their heads or not.

Let there be no compulsion in religion: Truth stands out clear from Error

For family I will go so far as holding hands, but don’t bow head or say amen at the end. Holding hands with a family member is not traumatic, and the moment (hopefully, some do go on) spent while they mumble some innate nonsense is little price to pay for family harmony. And if someone wants to call me out for not bowing my head, ask them what they were doing looking around! ?

For the most part family doesn‘t invite me to meals where prayer is included. it helps that different siblings and others have strayed to other sects and the differences between them are to them more important than their differences with a nonbeliever like me.

I'd handle prayer at meals in the same way that I handle broccoli. Let the people who want it have it so long as no-one's pushing it down my throat.

I don't think it's wrong to bow your head during such a thing..But you don't necessarily have to pray..Ill recite Shakespeare or sing.

Respect! For the home they are in, for the host, for the opinions of others. And then, when they have everyone over to their home, they can expect the same respect. I look at it as though I’m visiting a foreign nation; how would I act in a Kuwaiti’s home? Respectful.

My family asked me to say the prayer at our thanksgiving family dinner. I said "rub a dub, dub thanks for the grub". That was the last time they asked me to pray.
I told my children that my family likes to pray and we should hold still and be quiet while they pray. It is their belief not mine, but out of respect we should do this.

Same as I handle the national anthem and pledge of allegiance. I stand or sit silently and make no gestures of any sort. I show neither respect nor disrespect, but indifference

Mate, don't take it literally. The prayer is just a ceremony and it's good. Maybe in a way it acknowledges that 95% of the world doesn't have that roast turkey that you were delighting in eating. It's like saying thanks that I'm privileged and it washes all guilt away.
Don't worry about the symbolic prayer. It's cathartic. Look at it that way.

I don't bow my head or close my eyes. I just sit quietly and wait for them to finish their prayers.

Psychopathological
Rubbish
Aiding
Your
Evading
Reality  

This has always bothered me. People just assume that everyone thinks the way they do. Not once has anyone ever asked me if I wanted to join in their prayers. However, if I had guests over for a meal, you can bet someone would initiate prayer. I think religious people think it's their duty to do this and it somehow makes them superior.

I hold hands with them to be respectful and I sit quietly while they do their prayers I don't close my eyes. I don't bow my head. I just sit there or stand there and let them do their thing.

We are being respectful and tolerant of others, that is what humanists do. Use the time for silent reflection and appreciation of family, food, love and laughter. We give thanks and praise where it is warranted: On good decent folks.

I too have to explain to my kids why some of their friends perform this ritual, and that is how they see it. Like someone speaking to their partner in a foreign language, you wait politely until it is all over. I do not bow my head as this to me indicates compliance.
The one time I actually had a confrontation was when a friend, who knows my leanings, started to pray, in my kitchen over a meal I made. Right or wrong, I asked her to stop, she was in a house of unbelievers, and the person to be thanked was me, not her invisible friend. She demurred and thanked me......with a blessing. Sheesh !!!

I have no problem bowing my head when others do. I'm not there to impose my beliefs on others. I'm there to be with them as a social companion, so doing what works in that situation is my goal. I don't want my athiesm to interfere with my relations with others.

I much prefer your alternative - giving thanks to the actual, as opposed to mythical, provider(s) of the meal.
I was lucky, in that at boarding school we were a pretty irreverent bunch of wild colonial boys and whilst the housemaster or head prefect was saying grace in the dining hall, we would quietly chant things like "For what we are about to receive may the cook be severely punished."

I sit there with a smile, look around to see who else isn't bowing their head, and try not to laugh if I make eye contact.

What drives me bonkers is when religious people demand/expect us to just accept and respect what they believe, but they refuse to return the favor. It boils me. I don't bow my head at meal prayers period.

I think that, in my entire life, I was subjected to saying grace once at a dinner at my friend's place when I was a kid. It was one of the oddest experience I ever had.

To answer your question, I don't handle prayers or grace at my table. I cook, and I take pride in that. It's how I give back to the world. So, I say, good for you for not putting up for that hokem any longer.

If they are bowing their heads and closing their eyes, then you can do anything you want. I suggest shadow puppets.

I think the simple answer, we respect other beliefs even though we don't practice or believe them. Athiests are tolerant, sadly many religious people are not, a sad fact we have to live with, and the cause of many wars.

I recently visited my rather conservative Christian sister in Virginia for her 50th birthday. I hadn't seen her in nearly 8 years. "Grace" was said at every meal. I just sat there looking at everyone while they prayed. It was her house, so those were her rules. I just didn't participate. Those are MY rules. Praying aside, it was a GREAT visit.

I just stand quietly or wait til they're done to start eating. Participating in the ritual doesn't teach tolerance or respect. It teaches them that your (possibly their's) beliefs and rituals are not as important as everyone else's..