(It's nice to see how each response proposes much longer time than the previous one! )
Look up the intro for Heroes III on YouTube. It starts with Queen Catherine saying "Seven weeks have passed since we set sail from Enroth". So we can assume that the sail from Ironfist to Erathia (Steadwick?) takes 6-8 weeks, depending on how much time you lose by evading pirates and monsters (there's also a discussion about this at the Celestial Heavens, see the link).
We also know that it takes 1 week to sail from Steadwick to Evenmorn Islands. So I opened the map in GIMP, drew a rough path between the two places, and measured the length. The length was 3490 px, which makes it roughly 500 px = 1 day of sail.
So now we know Ironfist → Steadwick and Steadwick → Evenmorn. So now I just use some guesswork to guess a point X, which is where the paths Ironfist → Steadwick and Ironfist → Emerald Isle part. Then we getIronfist → Emerald = Ironfist → X + X → Emerald = Ironfist → Steadwick - X → Steadwick + X → Emerald. (1)
So now it's only a matter of more GIMP measurements. We find that X → Emerald = 3380 px = 6.8 days and X → Steadwick = 1158 px = 2.3 days, so, plugging into (1), we getIronfist → Emerald = 49 + 6.8 - 2.3 = 53.5 days.
Now New Sorpigal is pretty much on the way, and the sail from Ironfist to NS takes 2 days, so the final result is ~ 50 days (plus or minus troubles with pirates & comp.)