The following information is from my eBook on Type One Liberty Head Double Eagles at http://doubleeaglebook.com/
After producing nearly 20,000 1861-S Paquet reverse double eagles, the San Francisco mint was ordered to continue production using the old Longacre reverse. Three-quarters of a million were struck. The 1861-S is similar in overall rarity to the 1859-S and 1860-S, but it is rarer in higher grades.
STRIKE: The 1861-S is one of the weaker-struck Type One double eagles from the San Francisco mint. The obverse shows little distinct detail on the hair with the curls around the face and below the ear displaying little separation. The hair at the top of the head shows less than half of the detail and the bow is not distinct. The stars are mostly flat at the center and the denticles are not crisply defined as on earlier San Francisco double eagles. The reverse can show weakness at the horizontal lines in the shield, the stars above the eagle’s head, the wing tips and the tail feathers. On a few, the mintmark is not full at the top.
SURFACES: Most 1861-S double eagles are found with “scuffy” surfaces as the result of contact with other coins. Many are “net graded” by PCGS and NGC to reflect their lack of eye appeal as a result of dense, deep marks. Examples which show choice surfaces do exist but these are harder to find than most people realize.
LUSTER: This issue shows below average luster. On higher grade coins, the luster has a satiny texture with a slight grainy appearance. This date is easier to find now with decent luster than in the past and this is due to shipwreck coins; see below for more information.
COLORATION: The natural color tends to be either a medium orange-gold or rose-gold hue. This is a hard issue to find with natural color.
EYE APPEAL: This is an issue which has below average eye appeal. It is easier to find a decent looking coin than it was when the first edition of this book was written in 2002 but a CAC-quality 1861-S remains very scarce and should command a strong premium over an average quality coin.
INTERESTING VARIETIES: All known example have a Medium S mintmark. Most show a heavy date. A small number (around 10%) have a lighter date with small, wispy serifs on the 1’s. This variety is not considered to be collectible by specialists.
PROOFS: No proofs were struck.
HOARDS: A total of 81 were found in the S.S. Republic including 11 which were graded Uncirculated by NGC. There were 43 in the S.S. Brother Jonathan but most were in lower grades. Small groups of 1861-S double eagles are still found in Europe and other overseas sources.
BUYING TIPS: Nearly all of the higher grade 1861-S double eagles are from shipwrecks, although they may not be marked as such by PCGS or NGC. Try to distinguish between original surfaces and shipwreck surfaces when make a buying decision.
AUCTION RECORD: The current auction record for this date is $37,375 which was set by Heritage 1/12: 5038.
FINEST KNOWN: A PCGS MS63 in the Crawford collection is the finest 1861-S double eagle of which I am aware.
TOTAL KNOWN: 2000-3000+
Very Fine: 500-800
Extremely Fine: 1000-1500
About Uncirculated: 480-670
POPULATION FIGURES: As of the beginning of 2015, PCGS had graded three in MS60, eight in MS61, four in MS62, and one in MS63 for a total of 16 in Uncirculated. NGC had graded nine in MS60, 12 in MS61, and four in MS62 for a total of 25 in Uncirculated. This includes 11 coins in various Uncirculated grades from the S.S. Republic. These figures are slightly inflated, especially the MS60’s and MS61’s from NGC. CAC has approved five Uncirculated examples; two in MS60, one in MS61, and two in MS62.
PERFORMANCE SINCE 2002: In the current market, a choice About Uncirculated example of this date (equivalent to an AU55) is worth $4,500-5,500. When the first edition of this book was published in 2002, the same coin was worth $2,000-2,500. In the current market, an average quality Uncirculated example of this date (equivalent to MS61) is worth in the range of $16,000-18,000. In 2002, the same coin was worth $8,000-9,000. It is my opinion that the 1861-S is currently undervalued in nearly all grades and it has been outperformed in the last decade+ by less rare dates.
COMMENTS: The discovery of eleven Uncirculated 1861-S double eagles from the S.S. Republic treasure virtually doubled the total number of Uncirculated 1861-S double eagles. The 1861-S remains rare in Uncirculated with most in the MS60 to MS61 range. There are probably just five or six properly graded MS62’s and this date is unique in MS63.
David Akers (1975/88):
The 1861-S is scarce in all grades, on a par with the 1854-S, 1860-S, 1862-S and 1864-S among others. Compared to other S-Mint twenties, it is distinctly surpassed in overall rarity only by the 1861-S Paquet and the 1866-S No Motto. The majority of known specimens are well worn with F to EF being the typically available grades. In AU, the 1861-S is very scarce and in full mint state it is rare. Choice and gem uncirculated examples are very rare though not quite as "impossible" to obtain as similar quality examples of the 1864-S, 1866-S Motto and 1867-S to which the 1861-S is otherwise similar in overall rarity.