New member here as well, but I might just as well try to help.
I'm not completely sure what you're exactly aiming at, but actually, the concept of longitude and latitude is not too much younger than precise map making is, as the first instance we know of was a Greek astronomer in the 2nd century BC. I'm not sure though whether there are preserved sea-faring maps from that time, I would guess rather not. The only maps from ancient Greek and Roman times I can recall are usually less worried about overly precise distances etc. A famous one for example shows the whole known world, resized to fit on a scroll, hence is 680x34cm large - it couldn't be further from displaying true proportions, but it wasn't meant to, because it was supposed to show where the imperial and other main roads lead to from one place to another, along with rough distances from city to city. Geographical precision in a modern sense was not a value in itself for ancient maps in general, so from that example I would draw the conclusion that sea-faring maps of that time - IF they used maps at all, as opposed to relying on well-known routes they knew from routine - would probably focus on giving a pretty precise coastline to aid coastal navigation, as well as trying to give roughly the correct position of places, so you could e.g. navigate from Athens to southern Italy, from there to Sicily, Malta, and then Carthage. That's simply my guess, though. On open sea they'd probably rely on steadying the course based on the position of sun and stars. I'm not even too sure how much they relied on maps rather than traditional knowledge - after all, most of seafaring before longitude and latitude (to circle back to your initial question) took place on the Mediterranean sea or along coasts. Still it had its marvels, these men were pioneers of seafaring and had some great feats, like sailing around the southern tip of Africa. Hope it helped.