diff --git a/src/libraries/System.Net.Quic/src/System/Net/Quic/Implementations/MsQuic/MsQuicConnection.cs b/src/libraries/System.Net.Quic/src/System/Net/Quic/Implementations/MsQuic/MsQuicConnection.cs
index 7b0579e73c727..37998df2e9603 100644
--- a/src/libraries/System.Net.Quic/src/System/Net/Quic/Implementations/MsQuic/MsQuicConnection.cs
+++ b/src/libraries/System.Net.Quic/src/System/Net/Quic/Implementations/MsQuic/MsQuicConnection.cs
@@ -227,6 +227,7 @@ private static uint HandleEventConnected(State state, ref ConnectionEvent connec
 
                 state.Connected = true;
                 state.ConnectTcs!.SetResult(MsQuicStatusCodes.Success);
+                state.ConnectTcs = null;
             }
 
             return MsQuicStatusCodes.Success;
@@ -576,7 +577,8 @@ internal override ValueTask ConnectAsync(CancellationToken cancellationToken = d
                 throw new Exception($"Unsupported remote endpoint type '{_remoteEndPoint.GetType()}'.");
             }
 
-            _state.ConnectTcs = new TaskCompletionSource<uint>(TaskCreationOptions.RunContinuationsAsynchronously);
+            // We store TCS to local variable to avoid NRE if callbacks finish fast and set _state.ConnectTcs to null.
+            var tcs = _state.ConnectTcs = new TaskCompletionSource<uint>(TaskCreationOptions.RunContinuationsAsynchronously);
 
             try
             {
@@ -600,7 +602,7 @@ internal override ValueTask ConnectAsync(CancellationToken cancellationToken = d
                 throw;
             }
 
-            return new ValueTask(_state.ConnectTcs.Task);
+            return new ValueTask(tcs.Task);
         }
 
         private ValueTask ShutdownAsync(
@@ -683,9 +685,10 @@ private static uint NativeCallbackHandler(
 
                 if (state.ConnectTcs != null)
                 {
-                    state.ConnectTcs.SetException(ex);
-                    state.ConnectTcs = null;
+                    // This is opportunistic if we get exception and have ability to propagate it to caller.
+                    state.ConnectTcs.TrySetException(ex);
                     state.Connection = null;
+                    state.ConnectTcs = null;
                 }
                 else
                 {
diff --git a/src/libraries/System.Net.Quic/tests/FunctionalTests/MsQuicTests.cs b/src/libraries/System.Net.Quic/tests/FunctionalTests/MsQuicTests.cs
index 0d1ec65f00e79..0adb63860c4f3 100644
--- a/src/libraries/System.Net.Quic/tests/FunctionalTests/MsQuicTests.cs
+++ b/src/libraries/System.Net.Quic/tests/FunctionalTests/MsQuicTests.cs
@@ -152,7 +152,6 @@ public async Task CertificateCallbackThrowPropagates()
         }
 
         [Fact]
-        [ActiveIssue("https://github.com/dotnet/runtime/issues/56263")]
         public async Task ConnectWithCertificateCallback()
         {
             X509Certificate2 c1 = System.Net.Test.Common.Configuration.Certificates.GetServerCertificate();
@@ -235,7 +234,6 @@ public async Task ConnectWithCertificateCallback()
         }
 
         [Fact]
-        [ActiveIssue("https://github.com/dotnet/runtime/issues/56454")]
         public async Task ConnectWithCertificateForDifferentName_Throws()
         {
             (X509Certificate2 certificate, _) = System.Net.Security.Tests.TestHelper.GenerateCertificates("localhost");