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I'm fairly certain that it is illegal to download the ROMs for emulators, but I'm not a lawyer so don't quote me on that.
If you really want to get back into 16 bit gaming, check out the older videogame consoles on Amazon. You can get older videogame consoles and games there. That's probably your best bet if you want to skip the emulation thing. Run it on classic hardware. It's legal and you won't get into trouble.
It is very confusing to those who actually concern themselves with the law. For the most, it is illegal to download games (ROMs) yet downloading most emulators is completely legal (at least from the 16 bit era.)
Though you said that you have copies of these games, downloading the game is actually illegal. You are supposed to make your own back-up from your own game, even though the data you download from the internet is the exact same data you would obtain from doing the back-up yourself. However, even though downloading and using these games is technically illegal, you are very unlikely to actually get in trouble if you decide to emulate these games.
Maybe this will help:
I think that you have to actually own a physical copy of the game for it to be legal to use an emulated version. If you already own a copy, play on, player. If you don’t, then you are using an illegal copy of something that you don’t own. Perhaps someone else has greater insight, but I think that is the basic rule.