Below are some patches to remove the copy protection from both Ultima 7 games:
Ultima VII: http://patchery.net/patchery/patch.html?id=1000031
Ultima VII Part Two: http://patchery.net/patchery/patch.html?id=1000032

The patches are "non-obtrusive" - they modify the game data so that the conversation flows right past the copy protection and continues on. For example, in Serpent Isle when meeting the monk Thoxa for the first time, she transitions directly from "Even as was foretold [...] My name is Thoxa" to "Thou art truly the one that I seek!" without prompting for the copy protection answers.

--- APPLYING THE PATCH ---
Here are some instructions to apply the patches:
1. Navigate to one of the links above
2. Open the Ultima 7 "STATIC" directory in Windows Explorer (or equivalent for your OS). The directory is usually located at C:\GOG Games\Ultima VII - Complete\ULTIMA7\STATIC (or SERPENT\STATIC for Serpent Isle)
3. Drag the "USECODE" file from the "STATIC" directory into the drop zone on the open webpage in your browser
4. After it's finished analysing the file, click the "Download patched file" button to download a patched copy of the file
5. Rename the original copy of the "USECODE" file inside the "STATIC" directory to something like "USECODE.BACKUP"
6. Navigate to where the patched file was downloaded (varies depending on your web browser) and cut/paste the file into your "STATIC" directory


--- REMOVING THE PATCH ---
The patch can be removed by replacing the patched "USECODE" file with the backup that was created earlier. Alternatively, navigating to the patch page and dragging the patched version of the file into the drop zone will allow download of the unpatched file.


--- EXTRA VERIFICATION ---
To double-check that the right bytes were patched, you can run a binary comparison on the files using the "fc" tool from the Windows command prompt. The results should match up with the details on the patch webpage.

C:\>cd C:\GOG Games\Ultima VII - Complete\ULTIMA7\STATIC
C:\GOG Games\Ultima VII - Complete\ULTIMA7\STATIC>fc /b USECODE USECODE.BACKUP
Comparing files USECODE and USECODE.BACKUP
...

I keep getting an error "Could not find patterns in matched file." Does this still work?

That message usually means that you have a different version of the game (or file). I used the gog.com release to create the patch. Pressing "v" in game shows "ver 3.4" for the Black Gate and "Ver 1.02s5 Final" for Serpent Isle.

An alternative way of applying the patch is to use a hex editor (like UltraEdit) to manually modify the bytes according to the "Difference" sections listed on the patch page, but you would probably need to search for some near matches as the algortihm was unable to find the exact patterns in your file.

If you're happy to send through your USECODE file, I could try to apply the patch. You can email a zipped copy to gammadragon@hotmail.com

The website works on my version of the game, tested with Firefox, Chrome and IE11. I can also confirm that Ultima 7 can be fully completed after the patch is applied.

The website no longer exists, so I'm posting the patches here:

Ultima VII: The Black Gate

Filename: USECODE
Filesize: 1521368 bytes

Offset: 0x1420F0
Search for: 1C C4 0D
Change to: 06 0B 00

Offset: 0x14F1E9
Search for: 24 03 00 05 16 00 1C 0C
Change to: 06 -- -- -- -- -- -- --



Ultima VII part Two: Serpent Isle

Filename: USECODE
Filesize: 2103075 bytes

Offset: 0x564E1
Search for: 33 1C FB 01 33
Change to: -- 06 07 00 --

Offset: 0x828F9
Search for: 1C 26 35
Change to: 06 07 00

that does sound handy.

but what's the fun in playing Ultima VII without having to diddle with those little numeric slider controls to select precisely the value written in the manual or whatever?