Want to sell your old jewelry, particularly diamonds? On an average day recently, eight different companies advertised in the newspaper, urging people to trade their jewelry for cash.

"Do you have a Rolls Royce in your safe deposit box?" reads one large ad.

"Cash offer for your diamonds" and "We need diamonds and precious gems for our European and South American connections," other ads say.

Buying old jewelry -- what the industry calls "estate jewelry" -- is a multi-million-dollar business. Herbert Schoenberg, vice president of Balogh Jewelers, one of South Florida's oldest jewelry businesses, says estate purchases average between $15,000 and $20,000 each. Nationally, the average engagement solitate bought last year weighed about a half carat and cost $700.

One reason for both the interest in estate jewelry and the prices is that the value of diamonds is skyrocketing. At the end of August, diamond dealers received notification that the price of raw diamonds was going up 13 percent, and finished diamonds, 17 percent, in part because of their scarcity. Statistics from Solomon Brothers, a New York investment firm, show that diamonds have demonstrated a 12.6 percent compounded annual rate of return on investment over the last 10 years.

The local Better Business Bureau has received no complaints against companies advertising to buy estate diamonds. "We've watched it and seen it [the advertising] going, but we haven't had the complaints," says Art Hershbein, deputy director of the consumer division.

Still, because the estate jewelry business is so active, Hershnein and industry experts advise caution when selling diamonds and other jewelry. "Don't take your jewelry to someone who makes extravagant claims," Schoenberg says. "Ask around [for a jewelry or other market] just as you would for a doctor." There are three markets for old diamonds -- jewelry stores, diamond brokers and auction houses.

If you decide to sell, document your stone's approximate cash value, but remember that evaluating a diamond is subjective process. They are judged on four characteristics: carat (weight), cut (whether the cut reflects light well), color (generally, the less color the better), and clarity (the number of flaws). One appraiser, for example, may decide a stone is colorless. Another may see a tint.

The Gemological Institute of America (GIA) is the country's only impartial diamond evaluator. It has offices in New York and Los Angeles, and it will evaluate any unset stone weighting at least one carat. The charge for such evaluations is based on weight and begins at $65 for one carat, a spokesman says.

But the GIA won't talk money -- it won't tell you how much a diamond is worth. It will give you an internationally recognized certificate stating the stone's weight, color, cut and clarity. The certificate makes a good starting point for discussions of money when you begin to sell.

Industry spokesmen say you should be wary of local appraisers who claim theirs is a GIA evaluation. Even if they have been trained by the institute, their appraisal doesn't carry the weight of an official GIA certificate. To arrange a GIA evaluation, contact the institute; then you will have to send your diamond there.

You may have old appraisals of your jewelry that give you some idea of its value. The experts say an appraisal made for insurance purposes may be on the high side of a diamond's actual value, while an appraisal for estate purposes may be lower. In addition, such an appraisal may suggest a retail price. When you begin to sell, you'll be selling wholesale, not retail. The trick to selling your diamond is to get as near the retail price as possible. Halve the retail value to find the wholesale price.

Each market for your diamonds has its advantages and disadvantages. Here are some of them and also some tips for dealing with various markets.

Jeweler -- Selling to a jeweler can be the quickest way to get cash for your stones. Most jewelers will take 15 to 20 minutes to examine a diamond and make you an offer for it immediately. If you accept the offer, you can show your identification and take a check out of the store.

Brokers and representatives of auction houses say you may get only a half to two-thirds of a stone's wholesale value from jewelers, because they may not have a large resale market and because they're looking for a bargain.

If you want to sell quickly to a jeweler, ask around for a store with a good reputation. And take your stone to several different stores and ask for their best offers.

When you take a stone into a store, the jeweler may want to remove it from its setting if it is over one carat in weight. He should do this in front of you. He will also weigh the stone, measure it with a gauge and examine it under a microscope and light. Be wary if he offers you a price without such examinations, the experts say.

Some jewelers may offer to act as a broker of the stone for you. That means they will keep the stone in the store for several weeks and try to sell it to a retail customer. If they're able to sell it, they will take a 10 percent commission.

Auction Houses -- Selling a diamond through an internationally known auction house such as Sotheby Parke Bernet or Christie's may take two months or more. But the advantage to dealing with such an auction house, according to Dennis Scioli, head of jewelry sales for Sotheby in New York, is that your diamond is presented to a large group of potential buyers. Sotheby has monthly jewelry auctions in New York and one sale a year in Palm Beach, usually in late February or early March.

To sell through an auction house, contact one of its offices and a representative of its jewelry division will make arrangements to see the stone and evaluate it.

The auction house will take a 10 percent commission on the sale and the selling price is likely to fall somewhere between the stone's wholesale value and its retail one.

Brokers -- Most diamond brokers deal only on investment diamonds not jewelry stones. But David Rosental, president of Kohinoor Investment, Ltd., of New York, says his company will help individuals sell diamond jewelry. Rosental said such sales represents about a quarter of his company's multimillion dollar annual business.

Rosental says his company can usually sell a diamond for its wholesale value.

The company charges a 5 percent commission on the sale and a $2 fee for handling the stone and evaluating it.

If you contact Kohinoor, you'll be given literature about diamonds. Then the company will help you send your diamond to New York. The package will be opened before witnesses and given a laser scan which makes a fingerprint-like identification of the stone. A copy of the "gemprint," as it is called, is available to you from the company.

Then the company will evaluate the stone and attempt to sell it.