According to this blog post I’ve figured out, that I should create an SSL certificate and assign it to specific port (:99 in my case).
I’ve created locally signed SSL. Then got it’s Thumbprint and ApplicationId. Using CMD command netsh (in pre Win7 systems there is an httpcfg tool), I’ve assigned my certificate to the port
netsh http add sslcert ipport=0.0.0.0:99 certhash=3e49906c01a774c888231e5092077d3d855a6861 appid={2d6059b2-cccb-4a83-ae08-8ce209c2c5c1}, where certhash = SSL Thumbprint, and appid = ApplicationId I’ve copied earlier.
That’s it, now I’m able to make HTTPS requests!