SlimerJS (as of 0.8.3) lacks the commandline options of PhantomJS to say "relax about bad certificates". Unfortunately the self-signed SSL certificate, that developers typically use during development, counts as a bad certificate.
Here are the steps needed to handle this:
1. slimerjs --createprofile AllowSSL
Make a note of the directory it has created.
(You can call your new profile anything, "AllowSSL" is just for example.)
2. Go to normal desktop Firefox, browse to the URL in question, see the complaint, add it as a security exception.
Chances are, if you have been testing your website already, that you've already done this and you can skip this step.
3. Go to your Firefox profile, and look for the file called "cert_override.txt". Copy that to the directory you created in step 1.
4. Have a look at the copy you just made of "cert_override.txt".
If it only has the entry you added in step 2, you are done.
Otherwise, remove the entries you don't want.
(The file format is easy: one certificate per line.)
5. Now when you need to run slimerjs you must run it with the "-P AcceptSSL" commandline parameter.
E.g. "slimerjs -P AcceptSSL httpstest.js"
If you are using SlimerJS with CasperJS (requires CasperJS 1.1 or later), do the same, e.g.
casperjs test --engine=slimerjs -P AcceptSSL tests_involving_https.js