We offer one of the biggest and always up to date list of SSL supported free proxy servers.
These proxies are well known to support SSL connections. You can use them to access SSL/TLS encrypted services without worrying about connection security assuming your software properly handles certificate validation.
Just don't allow unverified certificates and you can consider connection secure even for sensitive data.
Keep in mind that target service you want to access must support encrypted connection (in case of websites it is https://)