Thanks for pointing me in the right direction. I must say that it took more than a quick search. Some of the hits are very long and convoluted, and some are actually about being out of disk space.
The important bit was to remove and then re-generate the certs. Do I understand this correctly, that having a certificate mismatch causes apache to complain about being out of disk space? They really need to fix their error messages I think.

Again, thanks for your patience and for the pointers. We have been running SME Server since 2007 with almost zero problems. A truly useful piece of software.