Extract SaveGame Manager GX to the root of your SD card or USB drive, and put it into your source Wii/Wii U.
Launch the Homebrew Channel, then launch SaveGame Manager GX.
Ensure that the source is set to Wii.
Find and select your save, then Extract, then Default.
Repeat this for the rest of the saves you would like to copy.
Press the HOME button and exit SaveGame Manager GX.
Put the SD card into the target Wii/Wii U.
Create a new save file for each game. This is needed so that SaveGame Manager GX can overwrite it.
Launch the Homebrew Channel, and launch SaveGame Manager GX.
Ensure that the source is set to your SD or USB.
Select each save you copied and click Install.
By importing your NAND backup into Dolphin, you effectively copy everything on your Wii (at the time of the backup).
This also has the benefit of allowing access to Wiimmfi, as well as carrying over RiiConnect24 patched channels.
If you have already done this, consider the SaveGame Manager GX method to save time.
If Dolphin is set to use a .raw memory card, use Tools > Memory Card Manager to export your desired saves to .gci.
Open Dolphin Emulator.
In the main menu, select File > Open User Folder.
In the folder that opens, navigate to GC > [Save region] > Card A.
Copy the .gci files you would like to put on your Memory Card.
Create a folder named MCBACKUP on your SD card or USB drive, and place the .gci files you copied into it.
Download and extract GCMM to the root of your SD card or USB drive.
Safely eject the SD/USB from your PC, then insert it into your Wii.
Launch the Homebrew Channel, then launch GCMM.
Select the device you have copied the .gci files to.
Press +/X to enter Restore mode.
Select the slot that has your Memory card.
Select the save you would like to restore.
If you would like to restore all the saves in MCBACKUP, press 1/R.
When restoration is complete, press any button to continue.
Instructions
Open Dolphin Emulator and select Tools > Memory Card Manager from the main menu.
Click the Open button next to Slot B.
Go to the saves folder on your SD card or USB drive, and select the .raw file named after the game's ID.
If you do not already have a save on Nintendont, select Create and set the Card size to 251 blocks.
If you are using one memory card for all games, open the ninmem.raw/ninmemj.raw file on the root of your SD/USB.
If Dolphin is storing your saves in a GCI folder (default):
Click Switch to B.
Click Import, and navigate to <REGION>/Card A/.
Select the .gci file(s) you would like to import. Otherwise, if Dolphin is storing your saves in a .raw file. simply select your saves on the left side and select Copy to B.
All methods here require a Wii with GameCube ports.