Thanks for your help Maxim, but I am afraid that I still can't get PUT to work.
File permissions are fine, so I assume that my nginx.conf is still wrong:

location calendar {
root html/calendar;
dav_methods PUT DELETE MKCOL COPY MOVE;
dav_access group:rw all:r;

limit_except GET {
allow 172.21.42.0/24;
deny all;
}

Which still produces '405 Not Allowed' with PUT (reading is fine)