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I can't provide personal experience- as I've never had a 3rd-party appraisal performed for my own collection, but your best choice would be searching the auction websites for "completed sales" which would provide you values of comparable items.   I would branch out beyond "Ebay"... there are several auction houses which have various mathematical/scientific instrument auctions yearly..  Auction Team Breker in Germany;  Skinner, Inc in the United States;;  Charles Miller in London, UK all have annual auctions with values of items sold (or listed as a range in the pre-sale auction catalog).     Contact me if you need assistance- I have copies of several auction catalogs from the past few years, I could provide my own estimate of several nautical categories of instruments/ ephemera/ items if needed.

Most important factor to the value of most instruments is their provenance, manufacturer, assessed survival rate and current rarity, and the presence/ or absence of any accompanying accessories, cases, manuals, etc.. which tend to be separated from the instruments over time.