Assuming your pearls are natural (not cultured) or reasonably large size (say, with a few over 5mm) and nice quality (light cream or white, roundish, lustrous).. you've got a treasure! Which means, you will have to look at high end buyers - antique jewelry seller and auctioneers that may not be local. No problem though - a first inquiry by e-mail is accepted these days and the potential value of the thing would be worth a train ticket or a dozen: a mention of reputable appraisal, a lab report help; sometimes pictures are required, always helpful.
A couple of links to such institutions:
Gemological laboratories recognized in auctions:
GIA,
AGTA
Jewelry auctioneers: a sort of 'top ten' given for
reference at GIA
And a couple of jewelry antiquarians with an interest in natural pearls that come to mind:
Lang,
Three Graces...
There are a couple of pearl business selling (and buying too, I would think) natural pearls on this forum:
Pacific Coast Pearls,
Pearl Paradise,
Kojima Pearl... I am probably missing a few. Take a deeper look at this section on
'Natural Pearls' on this forum.
Judging from the last 2-3 years worth of jewelry auctions, natural pearls have not been in such demand for decades! However, they are still a rarefied choice at the highest end, and less then perfect pieces are not as hot... It should be a good time to sell. But the local jewelers in a small town may be unable to help at all.
In all this, I'd start by writing to the potential buyers with the details on the appraisal report, giving the name and credentials of the appraiser (since you say it is a well knows one). Making some reference to a recent, similar auction lot ... and promising a lab report if necessary. At worst, you had lost time with a dozen e-mails.
I hate selling anything! But... how bad can it be? Also take a look at prices and assume that the seller does make a good percentage of that. Even so, it might be a pleasant surprise.
Now, I am assuming the pearls are natural. None of this applies to cultured pearls... I wouldn't know where to sell those other then Ebay either.