For NES, the main option is NES DS. For this, if you have a device explicitly supported by it, you can run *.nes files directly off your card. Otherwise you'll have to package the NES games into a *.nds file, and I can't guarantee that saving and savestates will work in that instance. Devices specifically supported by NES DS are slot-2 devices at the moment, though theoretically DLDI support is being added so all cards will be able to load .nes files directly from the card sometime in the future.
It's kind of a toss-up though, as I know that newer Supercards (especially Lites) have somewhat different hardware, and therefore won't work with NES DS unless you package the games in. Regardless, you'll be able to play the games perfectly fine with any device. It's just the saving and savestate support that may or may not work.
For SNES, your best bet is SNEmulDS, which runs on all devices that are supported by DLDI, including slot-1 devices like the M3 Simply and R4. There is support for large games through the use of a paging system that calls up 1-2 MB chunks of data into RAM as necessary, and saves and savestates should work fine on all devices. If you get a slot-2 card, you'll be able to run SnezziDS as well, which is a bit older but may run certain games better. SNES DS is the last option, though I wouldn't recommend it too much. With a slot-2 device you can use any size game you want in SNES DS, while with a slot-1 device the game must be below 2-3 MB so that the final filesize is under 4 MB.
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