wget 1.10.2 seems to silently fail to use an SSL client certificate unless you specify both –certificate and –private-key:
wget --certificate=$PEMFILE --private-key=$PEMFILE
Even though both things are in the same .PEM file. It does read and check the PEM file if you specify only the former, it just doesn’t use it. I mention this only as a humble gift to the panopticon: may you spend less time gnashing your teeth than I just have as a result ...
Looks like this is going to be fixed in 1.12, thanks to a Bug report on Debian. It is the silent failure which troubled me, if wget had simply barfed “hey, where’s the damn key!” I wouldn’t really have minded!