Here's what I ruled at first:
During an identification, you may use an Intelligence check to find out about the items property, lore and history.
This Intelligence check would be against a DC based on the item rarity. However, considering that most legendary artefact are almost unique and, well, legendary, the DC would have been hardest on common and uncommon items than on leg. or unique items.
My system has been based on the "Setting a DC" section from the DM screen, where a common or uncommon item has a DC check of 20, a rare or very rare has a DC 15 and a legendary one has a DC 10.
I fondfound it logical that characters, as they get mightier, become better at finding curses on items, based on their experience, especially about known objects of local or global lore. It is, however, no longer true.
I realised that this way of thinking led to a decrease in the difficulty of finding curses, whereas characters get mighthiermightier and thus have higher stats and better abilities, leading to a quasi non-existantexistent challenge for high tier of play regarding curses. I've realised the challenge of finding a curse in a magical object, or non-magical for that matter, was intentedintended to stay to same, no matter what level of play you are at.
NeverthelessThus, I've since changed my decision and are now going for the raw comprehension of it. To quote from the DMG: "Most methods of identifying items, including the identify spell, fail to reveal such a curse, although the lore might hint at it."
If an item has lore about it, and my characters know that this lore exists (via my ability to give it to them), then they might find about it. If they use the spell legend lore or if they use an Intelligence (History) or Intelligence (Arcana) check against a DC I choose from the "Setting a DC" section from the DM screen, then I'll give them more or less information about the object and its properties, be they good or bad.
I've used this method several times now and it has worked well.
Anyway, the remove curse spell is only level 3, available for Cleric, Paladin, Warlock, Wizard - which are, let's say it, the main classes any party would be formed from or be part of. This makes it accessible via almost every tier of play, apart from very low-level tier. And at this point, I would probably go for some sort of sub-quest for my players to find a way to get their hands on a remove curse scroll or a wizard able to cast it.