Retrieve HTTP response headers from WKWebview

It looks like you can access the response from the WKNavigationDelegate method webView:decidePolicyFor:decisionHandler:.

Set some object as the WKWebView's navigationDelegate, and add this method:

- (void)webView:(WKWebView *)webView decidePolicyForNavigationResponse:(WKNavigationResponse *)navigationResponse decisionHandler:(void (^)(WKNavigationResponsePolicy))decisionHandler {
    NSDictionary *headers = ((NSHTTPURLResponse *)navigationResponse.response).allHeaderFields;

    decisionHandler(WKNavigationResponsePolicyAllow);
}

Swift 3.1, 4, and 5 version of NobodyNada's answer:

Without force cast

func webView(_ webView: WKWebView, decidePolicyFor navigationResponse: WKNavigationResponse, decisionHandler: @escaping (WKNavigationResponsePolicy) -> Void) {
    if let response = navigationResponse.response as? HTTPURLResponse {
        let headers = response.allHeaderFields
        //do something with headers
    }
    decisionHandler(.allow)
}

With force cast:

func webView(_ webView: WKWebView, decidePolicyFor navigationResponse: WKNavigationResponse, decisionHandler: @escaping (WKNavigationResponsePolicy) -> Void) {
    let headers = (navigationResponse.response as! HTTPURLResponse).allHeaderFields
    //do something with headers 
    decisionHandler(.allow)
}

Swift 4.2 Answers with response.
func webView(_ webView: WKWebView, decidePolicyFor navigationResponse: WKNavigationResponse, decisionHandler: @escaping (WKNavigationResponsePolicy) -> Void)
 {
   let response = navigationResponse.response as? HTTPURLResponse
       decisionHandler(.allow)
}