There are a bunch of TG-16 and PC-Engine HuCards that can save... but you must either have a DUO or TG-CD (both of which have battery memory backup), or you need to purchase a TurboBooster Plus and plug it into the TG-16 expansion port (adding battery memory back up, as well as A/V jacks).
The Tennonoke Bank HuCard has a built-in battery (but it isn't a game, it's a "memory card"). Base 128 was another peripheral for saving games/backing up saves (but it plugged into the controller port, IIRC).
I don't recall if any regular HuCard game has a built-in battery.
There are advtantages and disadvantages to this system, by the way. By purchasing the Tennoke Bank card, you could go over to a friend's house and share your game saves (like memory cards we're familiar with today). BUT, if you didn't have a way of backing-up your game saves.... well, you'd be forced to delete some game saves to make room for new games.
The Tennonoke Card was never released in the US, so I had to buy an expensive converter in order to use it.
EDIT: I don't think I spelled Tennenoke correctly in this entire post. Not once!