configure Git to accept a particular self-signed server certificate for a particular https remote

Briefly:

Get the self signed certificate
Put it into some (e.g. ~/git-certs/cert.pem) file
Set git to trust this certificate using http.sslCAInfo parameter

In more details:

Get self signed certificate of remote server

Assuming, the server URL is repos.sample.com and you want to access it over port 443.

There are multiple options, how to get it.

Get certificate using openssl

$ openssl s_client -connect repos.sample.com:443

Catch the output into a file cert.pem and delete all but part between (and including) -BEGIN CERTIFICATE- and -END CERTIFICATE-

Content of resulting file ~/git-certs/cert.pem may look like this:

Get certificate using your web browser

I use Redmine with Git repositories and I access the same URL for web UI and for git command line access. This way, I had to add exception for that domain into my web browser.

Using Firefox, I went to Options -> Advanced -> Certificates -> View Certificates -> Servers, found there the selfsigned host, selected it and using Export button I got exactly the same file, as created using openssl.

Note: I was a bit surprised, there is no name of the authority visibly mentioned. This is fine.

Having the trusted certificate in dedicated file

Previous steps shall result in having the certificate in some file. It does not matter, what file it is as long as it is visible to your git when accessing that domain. I used ~/git-certs/cert.pem

Note: If you need more trusted selfsigned certificates, put them into the same file:

-----BEGIN CERTIFICATE-----
MIIDnzCCAocCBE/xnXAwDQYJKoZIhvcNAQEFBQAwgZMxCzAJBgNVBAYTAkRFMRUw
...........
/27/jIdVQIKvHok2P/u9tvTUQA==
-----END CERTIFICATE-----
-----BEGIN CERTIFICATE-----
AnOtHeRtRuStEdCeRtIfIcAtEgOeShErExxxxxxxxxxxxxxxxxxxxxxxxxxxxxxw
...........
/27/jIdVQIKvHok2P/u9tvTUQA==
-----END CERTIFICATE-----

This shall work (but I tested it only with single certificate).

Configure git to trust this certificate

$ git config --global http.sslCAInfo /home/javl/git-certs/cert.pem

You may also try to do that system wide, using --system instead of --global.

And test it: You shall now be able communicating with your server without resorting to:

$ git config --global http.sslVerify false #NO NEED TO USE THIS

If you already set your git to ignorance of ssl certificates, unset it:

$ git config --global --unset http.sslVerify

and you may also check, that you did it all correctly, without spelling errors:

$ git config --global --list

what should list all variables, you have set globally. (I mispelled http to htt).

OSX User adjustments.

Following the steps of the Accepted answer worked for me with a small addition when configuring on OSX.

I put the cert.pem file in a directory under my OSX logged in user and thus caused me to adjust the location for the trusted certificate.

Configure git to trust this certificate:

$ git config --global http.sslCAInfo $HOME/git-certs/cert.pem