How do I accept a self-signed SSL certificate using iOS 7's NSURLSession

Both connection:canAuthenticateAgainstProtectionSpace: and connection:didReceiveAuthenticationChallenge: are deprecated in iOS 8 anyway so you should use other methods.

What I am using in my projects is a delegate method of NSURLSessionDelegate. Adhere to that protocol then add this method:

func URLSession(session: NSURLSession, didReceiveChallenge challenge: NSURLAuthenticationChallenge, completionHandler: (NSURLSessionAuthChallengeDisposition, NSURLCredential!) -> Void) {
    completionHandler(NSURLSessionAuthChallengeDisposition.UseCredential, NSURLCredential(forTrust: challenge.protectionSpace.serverTrust))
}

Then, when you use initialize NSURLSession with delegate set to self. For example:

var session = NSURLSession(configuration: configuration, delegate: self, delegateQueue:NSOperationQueue.mainQueue())

Then use that session instance to call dataTaskWithRequest method on:

var task = session.dataTaskWithRequest(request){
    (data: NSData!, response: NSURLResponse!, error: NSError!) -> Void in
    if error != nil {
        callback("", error.localizedDescription)
    } else {
        var result = NSString(data: data, encoding:
            NSASCIIStringEncoding)!
    }
}
task.resume()

Complete working example can be found here.

For security reasons, if you use a self-signed certificate I recommend also implementing public key pinning (https://gist.github.com/edwardmp/df8517aa9f1752e73353)