Okay, I see that you are in Austin, TX, so the following might not apply. Still, my common sense tells me that a very similar scenario applies to the US, too.
They have a lot of these ads on TV in Germany, too, so one of our public TV shows about money* tested them. They first went to a certified appraiser, who made three tests bags with a value of 5 000 Euros. They sent the bags to different agencies from TV ads and also went to several Jewellers.
The send-in-by-post agencies offered one quarter to one half of the worth. The brick-store jewellers offered one half of the worth. None came close to the real worth.
So the advice was: shop around, but most importantly, if a jeweller appraises your stuff for free, he will cheat you on the price he pays you. Even if you have to pay the licensed appraiser a fee beforehand, you get an honest expert opinion by somebody who has no interest in lying to you.
Also, very important with jewelery, esp. old one: the worth can be far more than the net weight, because it’s art, and might be rare. That, like other art, depends on finding a seller wanting that piece, but it means, esp. if you are not in a hurry, to never melt down or sell for only the gold weight, but find out the real (relative) worth and try to get close to that.
You might also, besides jewellers, look at some specialist magazines or conventions of people who are interested in old jewelry, once you know the worth, and maybe sell directly there.
*Public TV in Germany is VERY DIFFERENT from US TV in terms of repubatibility, so please, no comments along “Don’t trust TV, it’s all on the level of Fox or CNN”, because it’s not. Think more BBC.