Maine liked Ike im 1956, when he received 70.87% of the vote.
Data doesn't exist on this site before 1856 but I have read that Ike's 1956 showing set a Maine record for Presidential elections, and it was only a two-way race so it couldn't have set a percentage margin record without setting a percentage record, and I doubt any credible author would call a largerer percentage margin 100+ years before as a smaller margin because the raw vote margin was lower when there were less than as many voters back then. See
https://uselectionatlas.org/RESULTS/compare.php?year=2004&fips=23&f=0&off=0&elect=0&type=state for more info, although it might not show up properly if you're not a member.