I usually say something akin to:
"Look, please don't hold back while speaking, just make an effort. I swear I won't laugh at you or judge you; I'm just here to help you. Don't worry about making mistakes. Native speakers of English make mistakes all the time! Shakespeare: the greatest English writer and the greatest writer of English, couldn't even spell his own name consistently. So please, do your best and try your hardest."
It sounds noble but I rarely actually follow it myself. I don't mean that I laugh at the students and call them morons—at least I don't do it to their faces. (JOKE!!!) I mean that I am very shy about speaking Polish, especially with a Polish person.
It's been said that one learns a language best while drunk, because it takes away inhibitions and makes one not afraid to make mistakes. I personally find this to be true, but I have trouble remembering what mistakes I made and what I actually said in general.
Now, here's a story:
When asking someone how to say something, I usually don't remember it very well. So, if asking, "How do you say 'girl'?" and someone replied "dziewczyna", I would have trouble remembering "dziewczyna."
I was in Germany and had some tsuika (Romanian moonshine made from plums.) I was getting 'festive' and asked a Pole next to me how one should say cheers. She said, "na zdrowie." To which I meant to reply, "I'll ask you again." (in Polish) but instead said, "Zapamietam Cie zawsze." She laughed and said, "Do you know what you just said?" I looked sheepish and said, "What?"
"You just said 'I'll remember you forever!'" We had a laugh and I quickly said, "Uh, I meant: Zapytam Cie znowu."
Again and again I am faced with a language barrier that seems to insurmountable for me. I'm not one of those people who can conquer a language easily and confidently (I got straight Cs in Polish, and I did actually try.) There are plenty of times I end up looking foolish when a person asks me a simple question and I do something totally unrelated to it. (Once, a security guard asked me to write down my last name and I wrote, "Hey, it's me! Come on down!" He gave me the queerest look and repeated the question several times.)
I'm not exactly confident in my abilities (there are uncountable episodes, in which I have embarrassed myself trying to speak/understand Polish) and I'm not very comfortable carrying on a conversation. Flaws I'd like to work on.
No matter how well you think you know a language (even your native one) someone or something is going to come along and show you something you'll never understand. Why people enjoy James Joyce is that thing for me.
And so, even though I get paid to coax people along and to be comfortable with the Mother Tongue, I understand where they are coming from, and have been there too many friggan times myself.