Well, I think I finally got the Windows 7 partition on my MacBook backed up.  The support staff at Paragon told me that their product, Drive Backup Pro 10, couldn't back up under Windows (using either Volume Shadow Service or their "Hot" technology).  What I had to do, they said, was use the CD recovery drive and run it from there.
So I did, and it appeared to work.   However, there's no way to be sure unless and until I attempt a restore, and I do not do restores lightly.
But my confidence grew today when I successfully used the Drive Backup Pro recovery disk to "upsize" the main drive on my webserver.  Yesterday I used the program to back up the boot drive on it, but it reported an unrecoverable read error.  Luckily, it only reported one.  So I hit "Ignore" and carried on.  Then I went to Hard Drives Northwest and bought one of a vanishing stock of new EIDE drives.  After installing it as the primary, I partitioned the new drive and restored the full partition backup.
At almost every step there were errors that could have been better explained.  I wondered, for example, why it reported read errors when an extensive "chkdsk" (check disk) found nothing.   In addition, the boot disk program reported read errors on the BACKUP drive until I partitioned and formatted the new C: drive.   After that, it ran flawlessly.
So now I have a new drive in my server, and about a 70% confidence level that I'm fully backed up on my dual-boot Mac.  As an intelligent consumer, what I really want is programs that give intelligible errors.  For example, why couldn't Paragon's program simply have an error message saying, "Live (hot) backup not supported under Bootcamp.  Please use recovery boot disk image."  That would have saved me literally hours of nonsense.
Oh, well.

Backing up a MacBook running BootCamp is no walk in the park.  WinClone, the most viable candidate, is no longer being supported.  Its author says that Windows 7 challenges have prevented him from continuing his work.

I just installed another possible candidate, Paragon software's "Backup Pro 10".  After a failed download, I got the product installed.  I tried three times to backup my Windows logical boot drive, and every time the product failed.  First, using Window's  "Volume Shadow Copy" service, I got error 0x11112 every time.  Then I switched technology to Paragon's "Hot Backup" capability.  It, too, failed, with error 0x1200e. 

Googling around (as always) I found that I was not alone-- many blogs and fora had notes about VSS error 0x11112.   Interestingly, the search engine at Paragon didn't have a SINGLE result for error 0x11112.  Why is it that vendor's so-called "support" websites don't find anything of value?  I've had the same problem with HP, among several others I could name.

So far, bah, humbug!