Natural, unheated ruby of fine color and good clarity goes for around $4000/ct and up in one carat sized, just to use a very rough approximation from the IGS value guide. So, potentially you could be looking at US$150,000 or even twice that or more at retail. Because there are so many factors involved, you really have to seek out a certified gemologist appraiser to get anything more than a wild guess, which is what I have given you.
Just to give you an idea of what is involved, each stone must be examined and measured and the weight estimated. Each stone has to be graded as to color and clarity. Each stone has to be examined for evidence of treatment. Even though you have been told they are untreated rubies, the only way a good appraiser will set a price and put his reputation behind it is to check for heating and treatments and even natural vs synthetic Once all this is done, the appraiser can find a price for the individual stones and also look at the gold quantity involved in the settings and the skill and artistic value of the setting. The appraiser will use more than one method of valuation. He or she will use a “bricks and mortar” valuation adding the value of the stones, gold, and cost of the assembly and stonesetting. Then he will also look at recent sales of similar pieces, In the case of a piece as large and expensive as this, probably he’ll look mostly at fine auction catalogs and records of sale going back at least ten years.
Another issue here is what type of appraisal you want. An insurance replacement value is different from a salvage value or a wholesale sale to a fine jeweler and that is still different from an auction sale or a private sale at retail(in a store or through a private sale). The market in which you are dealing determines the price, to some extent. Insurance replacement might be the most expensive, because the jeweler would have too find 38 matched rubies and do all the gold work, and it could be very difficult to find just the 38 stones required within a year at a decent price, just for starters. A retail auction price might be next, if folks are buying for themselves (retail)rather than as dealers/jewelers for resale. A salvage value would probably be lowest.
You should seek an independent appraiser who is not involved in sales, someone who does only appraisals, as they will have no interest in valuing low and steering you to someone who will buy. A Certified Master Gemologist appraiser certified by the American Society of Appraisers or one certified by the American Gem Society as an Independent Certified Gemologist Appraiser (ICGA) would have the right credentials and there are a couple of other certification organizations. You might inquire of the fine arts dept. at one of the big auction houses such as Southeby’s or Chrisite’s or of Tiffany’s or Bulgaris to get some names. they should be able to give you a list of names rather than someone in house. An appraiser can also advise you as to how to sell these, if that is your aim. Since errors could cost you thousands of dollars, you might seeks someone who will have a consultant or two in doing the appraisal or even seek two appraisals. because of the amount of work, the degree of experience and tools required and the degree of responsibility involved, this is not a $100 appraisal. A good appraiser should be able to put you at ease and discuss his/her methods and charges before proceeding.