How much should I expect to pay for a hand-drawn portrait of two children?

It depends on things like: what area you are in, did you contract her to do this work professionally or is she a "friend" of yours, how did you decide to use her, etc.

Since it is 'art' there is no real low or high cost. If I only knew her by hiring her to do this work and her portraits are truly very well done, in my area I would expect to pay at least $250 for an 11 x 14. I would consider that dirt cheap.

I'd tell her to name her price beforehand and we'd stick with it.

There's no way to put an official price on something like that. It depends on how good the artist is.

Ask her how much she would charge. Ask to look at other portraits like this that she's done. Then decide whether it's worth it to you.

sometimes artists charge by they number of hours they spent creating the piece, as well as cost of the materials and the size of the work. Is the artist matting and framing the work? I would find out, matting and framing almost always costs more than the artwork itself. Expect to pay about $300 at the most, but that would be alot considering they don't have alot of experience in portraiture. You can always look up this type of service on the internet and see what the going rate is.

why are you paying for a drawing when you could pay to get some really great professional photos taken? it sounds so outdated.

Sounds like one penny would be too much.

if the children looks happy,, it worth less than nothing, and if they are crying in the portrait,, worth at least one million $.

It is whatever price she tells you, art is art.