diff --git a/src/bitcoin-cli.cpp b/src/bitcoin-cli.cpp
--- a/src/bitcoin-cli.cpp
+++ b/src/bitcoin-cli.cpp
@@ -373,17 +373,12 @@
 
     // Get credentials
     std::string strRPCUserColonPass;
+    bool failedToGetAuthCookie = false;
     if (gArgs.GetArg("-rpcpassword", "") == "") {
         // Try fall back to cookie-based authentication if no password is
         // provided
         if (!GetAuthCookie(&strRPCUserColonPass)) {
-            throw std::runtime_error(strprintf(
-                _("Could not locate RPC credentials. No authentication cookie "
-                  "could be found, and RPC password is not set.  See "
-                  "-rpcpassword and -stdinrpcpass.  Configuration file: (%s)"),
-                GetConfigFile(gArgs.GetArg("-conf", BITCOIN_CONF_FILENAME))
-                    .string()
-                    .c_str()));
+            failedToGetAuthCookie = true;
         }
     } else {
         strRPCUserColonPass = gArgs.GetArg("-rpcuser", "") + ":" +
@@ -430,13 +425,30 @@
     event_base_dispatch(base.get());
 
     if (response.status == 0) {
-        throw CConnectionFailed(strprintf(
-            "couldn't connect to server: %s (code %d)\n(make sure server is "
-            "running and you are connecting to the correct RPC port)",
-            http_errorstring(response.error), response.error));
+        std::string responseErrorMessage;
+        if (response.error != -1) {
+            responseErrorMessage =
+                strprintf(" (error code %d - \"%s\")", response.error,
+                          http_errorstring(response.error));
+        }
+        throw CConnectionFailed(
+            strprintf("Could not connect to the server %s:%d%s\n\nMake sure "
+                      "the bitcoind server is running and that you are "
+                      "connecting to the correct RPC port.",
+                      host, port, responseErrorMessage));
     } else if (response.status == HTTP_UNAUTHORIZED) {
-        throw std::runtime_error(
-            "incorrect rpcuser or rpcpassword (authorization failed)");
+        if (failedToGetAuthCookie) {
+            throw std::runtime_error(strprintf(
+                _("Could not locate RPC credentials. No authentication cookie "
+                  "could be found, and RPC password is not set.  See "
+                  "-rpcpassword and -stdinrpcpass.  Configuration file: (%s)"),
+                GetConfigFile(gArgs.GetArg("-conf", BITCOIN_CONF_FILENAME))
+                    .string()
+                    .c_str()));
+        } else {
+            throw std::runtime_error(
+                "Authorization failed: Incorrect rpcuser or rpcpassword");
+        }
     } else if (response.status >= 400 && response.status != HTTP_BAD_REQUEST &&
                response.status != HTTP_NOT_FOUND &&
                response.status != HTTP_INTERNAL_SERVER_ERROR) {
diff --git a/test/functional/interface_bitcoin_cli.py b/test/functional/interface_bitcoin_cli.py
--- a/test/functional/interface_bitcoin_cli.py
+++ b/test/functional/interface_bitcoin_cli.py
@@ -37,15 +37,23 @@
         self.log.info("Test -stdinrpcpass option")
         assert_equal(0, self.nodes[0].cli(
             '-rpcuser={}'.format(user), '-stdinrpcpass', input=password).getblockcount())
-        assert_raises_process_error(1, "incorrect rpcuser or rpcpassword", self.nodes[0].cli(
+        assert_raises_process_error(1, "Incorrect rpcuser or rpcpassword", self.nodes[0].cli(
             '-rpcuser={}'.format(user), '-stdinrpcpass', input="foo").echo)
 
         self.log.info("Test -stdin and -stdinrpcpass")
         assert_equal(["foo", "bar"], self.nodes[0].cli('-rpcuser={}'.format(user),
                                                        '-stdin', '-stdinrpcpass', input=password + "\nfoo\nbar").echo())
-        assert_raises_process_error(1, "incorrect rpcuser or rpcpassword", self.nodes[0].cli(
+        assert_raises_process_error(1, "Incorrect rpcuser or rpcpassword", self.nodes[0].cli(
             '-rpcuser={}'.format(user), '-stdin', '-stdinrpcpass', input="foo").echo)
 
+        self.log.info("Test connecting to a non-existing server")
+        assert_raises_process_error(
+            1, "Could not connect to the server", self.nodes[0].cli('-rpcport=1').echo)
+
+        self.log.info("Test connecting with non-existing RPC cookie file")
+        assert_raises_process_error(1, "Could not locate RPC credentials", self.nodes[0].cli(
+            '-rpccookiefile=does-not-exist', '-rpcpassword=').echo)
+
         self.log.info("Make sure that -getinfo with arguments fails")
         assert_raises_process_error(
             1, "-getinfo takes no arguments", self.nodes[0].cli('-getinfo').help)