Gem Shopping Network is a legitimate business. They have been in business since 1997 and have an A+ Better Business Bureau rating. They have a variety of vendors who bring in their jewelry, some of which is VERY high end. They sell new, estate, and loose gemstones. The hosts and vendors are very knowledgeable, they give a lot of info on each piece (gemstone size/weight, # grams of gold/platinum, etc.) and I've learned a lot watching.
I have shopped with them for maybe 8 years or so and purchased a number of things. I have returned a few items (following their return instructions) and have never had a problem getting a timely refund.
The one thing I would caution is that their shipping fees are VERY high and if you do need to return, the shipping and insurance can really add up.
In the past couple of years, many of the hosts have adopted a very loud and excited sales manner, which I don't particularly like, but, maybe, they think this increases sales. Usually I just lower the volume on my remote.