As a person in the history field, I hear this question a lot. Sometimes I explain to a tour group that we can't touch anything in the rooms, because most of the furniture is over 200 years old. Someone, either adult or child, will invariably point to an object and ask "What is it worth?"
"This object gives historians a lot of information about how people lived in the 1700s. This information was not recorded in books and therefore it is of considerable value to historians."
That's not what they want to hear. They will then clarify their question as if I didn't understand, "How much money is it worth?"
I don't know if it is today's economy, but lately historical artifacts seem to be about the money that can be made. Shows like American Pickers, Pawn Stars, American Digger and many others put an emphasis on the price tag of antiques instead of their educational, historical and cultural value. It is an even more grave situation, when people are prompted to loot historic sites, like what happened in
Gettysburg two weeks ago.
It's really important for history educators to go over the basics of archeology and the importance of artifacts and antiques to our understanding of history. Tell your listeners the importance of the information gained from archeological sites and how the artifacts collected are not the goal, but a result of archeologists excavating for information. Try to bring the focus off the antiques and artifacts and try to emphasis how important these things are for learning about the past.

It's almost never good to put a monetary value on an antique in front of a crowd. Many people have the notion that antiques are worth huge sums of money, and some are. But, most antiques are pretty modest in price compared to the impression many get from Antiques Roadshow. If you tell your crowd that your dug Civil War Eagle Coat button is only monetarily worth about $6.55, many will be surprised at the low "value" but many more won't have an interest in holding it because it's no longer special in their eyes. Putting a monetary value on these things breaks the connection with the past that each individual can make when touching and passing them around.
Has anyone else noticed this at events and in museums? If someone asks you about the "value" of something, what do you say?