Proof 1857 Large Cents are known only of the Small Date versions. In particular, only Newcomb 3 and Newcomb 5 have been found in Proof; not surprsingly, they are both Proof-only varieties (no "business" strikes are known of either). Breen suggested that over 80 Proof examples of Newcomb 3 survived and that "at least a dozen" of Newcomb 5 survived. Both estimates are perhaps a little low, although the Newcomb 5 is indeed a rare coin.
Finest among the Proof 1857 Large Cents is a PCGS PR66RB, followed by a small group of PCGS PR66BNs. Red-Brown 1857 Large Cent Proofs are only slightly rarer than the Brown versions, but Red examples are exceedingly rare.
The most valuable Proof 1857 Large Cent is the PCGS PR65RD example from an early iteration of the Eugene Gardner Collection (1965), which sold in 2008 for $74,750