The information you have received is all very good and comes from some excellent agents in the area. I would like to add that if you are attempting to determine the value of your own home using an appraiser, that is great. It should give you the professional opinion you need to help you in establishing a reasonable price for your home if you are considering selling it soon. If on the other hand you are attempting to determine the value of home that may be a FSBO, then you will need to get the approval of the homeowner before an appraiser can do their job. If this is the case and you are not working with an agent to help guide you with respect to estimated home value before making an offer then I suggest contacting a local agent to help you. In fact using an agent will probably save you money in the long run as I have never seen a FSBO that is under priced.
As a significant amount of my business comes from the Chesterfield area I would be happy to assist you with this. At a minimum contact me and we can discuss your particular situation.

Fees to an independant appraiser might run around $300-$350.

I would concur with Keith, while it can be nice to know what the appraiser has to say, be aware that there are different appraisals for different reasons - the bank is looking to see if the home will appraise for as much as they are lending the buyer and their appraisers are currently only looking a 3 months worth of data in many cases. Again, as Keith noted, a bank will only accept their own appraiser's report. An insurance company is looking at replacement value in case they have to rebuild a house that is destroyed. A realtor looks at what a home is worth in the current market - 3 different values which MAY be the same, but often aren't. While you can say in marketing that a home is worth "x" amount, in reality, a home is worth what someone is willing to pay for it. I often have someone tell me that they "just recently" had an appraisal done due to a bank refinance, etc, and their home is worth X amount and that's what they want to list it at, and I have to explain that they can list it at that point, but don't expect to sell there, because that's not what the market is doing.

I recommend Mary Laudon at 314-780-2348. She is an excellent appraiser. She use to be a Realtor so she can look at it from that angle also..

Matt
My only question is why?
If this involves a purchase, you should know that Appraisers are under scrutiny by underwriters. I you are a seller and received the bad news that your home appraised for less than the purchase price, you have an uphill battle. A lender will not likely accept another appraiser's opinion unless there is something that the first appraiser missed in their appraisal.

If you are a buyer and you get a lower appraisal than the purchase price agreed, be thankful. Unless there is an error it is likely that the appraisal is correct.
Many times this occurs with owners selling without professional representation because nobody in the transaction really knows the true market value until the lender sends their appraiser.

Feel free to post more information or re-post another question that has more information.

When I represent either buyer OR seller I try to meet the appraiser and provide them with extra data that supports the price. Two weeks ago I met with an appraiser and upon discussing the property she asked me if I had a copy of the building permit for the addition (which I happen to have). If I did not she was not going to provide me with credit for that additional square footage.

I recommend Scott Wachter with Cardinal Appraisal. His number is 314.504.8841. I've recommended Scott to many others and they've always been happy with his work.