Very good point about the lack of records from time periods before there was actually DNA testing.

The only thing I can think of, if it's a "He Said, She Said" scenario (as far as whether sexual intercourse occured), is for the state to arbitrate it by saying: "We're requesting that both of you get DNA testing for purposes of identifying paternity. If Male Claimant tests positive for paternity, then he was obviously lying in order to shirk responsibility and he must reimburse the state for all testing expenses; if Male Claimant tests negative for paternity, then Female Claimant was obviously lying in order to create a false identity of the biological father and she must reimburse the state for all testing expenses." This would be the only way to keep both parties honest, and to actually prove their honesty (or lack thereof).