diff --git a/src/DiffEngine.Tests/ViewerProtocolTests.cs b/src/DiffEngine.Tests/ViewerProtocolTests.cs
index 8f681826..d136f18b 100644
--- a/src/DiffEngine.Tests/ViewerProtocolTests.cs
+++ b/src/DiffEngine.Tests/ViewerProtocolTests.cs
@@ -984,6 +984,61 @@ await Assert.That(await ViewerClient.SendAsync(new(ViewerVerb.List), default, po
             .IsEqualTo(SendOutcome.NoOwner);
     }
 
+    /// <summary>
+    /// A connect given up on is disposed while still pending, and the task behind it faults
+    /// afterwards with nobody left to observe it. The finalizer then reports it: in a test process
+    /// that launched a viewer, once per probe the launch gate made while the viewer was still
+    /// binding, and fatally in a host that treats unobserved task exceptions as fatal.
+    /// <para>
+    /// A zero wait gives up on every connect, whatever the platform does with a port nothing is
+    /// listening on - Windows lets it hang, others refuse it, both only after the wait has returned.
+    /// Serialised with the other tests in this class, since the event is process wide.
+    /// </para>
+    /// </summary>
+    [Test]
+    [NotInParallel]
+    public async Task AConnectGivenUpOnIsObserved()
+    {
+        ViewerServer.TryBind(0, out var server);
+        var port = server!.Port;
+        server.Dispose();
+        ViewerClient.ForgetUnowned();
+
+        var unobserved = new List<Exception>();
+        void Record(object? sender, UnobservedTaskExceptionEventArgs args)
+        {
+            lock (unobserved)
+            {
+                unobserved.Add(args.Exception);
+            }
+        }
+
+        TaskScheduler.UnobservedTaskException += Record;
+        try
+        {
+            for (var attempt = 0; attempt < 5; attempt++)
+            {
+                ViewerClient.TrySend(new(ViewerVerb.List), out _, port, TimeSpan.Zero);
+            }
+
+            // Long enough for the abandoned connects to fault, then collected so their tasks
+            // are finalized, which is when an unobserved fault is reported
+            for (var pass = 0; pass < 5; pass++)
+            {
+                await Task.Delay(200);
+                GC.Collect();
+                GC.WaitForPendingFinalizers();
+            }
+        }
+        finally
+        {
+            TaskScheduler.UnobservedTaskException -= Record;
+            ViewerClient.ForgetUnowned();
+        }
+
+        await Assert.That(unobserved).IsEmpty();
+    }
+
     [Test]
     public async Task AnAbsentOwnerIsNotAnError()
     {
diff --git a/src/DiffEngine/Protocol/ViewerClient.cs b/src/DiffEngine/Protocol/ViewerClient.cs
index 9e091597..2b3b68a0 100644
--- a/src/DiffEngine/Protocol/ViewerClient.cs
+++ b/src/DiffEngine/Protocol/ViewerClient.cs
@@ -164,7 +164,7 @@ public static bool IsOwned(int? port = null)
         try
         {
             using var client = new TcpClient();
-            owned = client.ConnectAsync(IPAddress.Loopback, endpointPort).Wait(ShortTimeout);
+            owned = Connect(client, endpointPort, ShortTimeout);
         }
         catch (Exception exception)
             when (Ignorable(exception))
@@ -223,7 +223,7 @@ public static bool TrySend(
         try
         {
             using var client = new TcpClient();
-            if (!client.ConnectAsync(IPAddress.Loopback, endpointPort).Wait(deadline))
+            if (!Connect(client, endpointPort, deadline))
             {
                 Found(endpointPort, false);
                 return false;
@@ -385,6 +385,30 @@ public static async Task<SendOutcome> SendAsync(
         }
     }
 
+    /// <summary>
+    /// A connect waited on for at most <paramref name="wait"/>. One given up on is still pending
+    /// when the caller disposes the client, and faults once that tears it down - or, where the
+    /// port refuses rather than hangs, when the refusal arrives - with nobody left to observe it.
+    /// The finalizer then reported it as an unobserved task exception: once per probe the launch
+    /// gate made while a viewer it had just started was still binding, in a test process that may
+    /// treat those as fatal. Observed here instead, since there is nothing to do with the fault.
+    /// </summary>
+    static bool Connect(TcpClient client, int port, TimeSpan wait)
+    {
+        var connecting = client.ConnectAsync(IPAddress.Loopback, port);
+        if (connecting.Wait(wait))
+        {
+            return true;
+        }
+
+        connecting.ContinueWith(
+            static _ => _.Exception,
+            Cancel.None,
+            TaskContinuationOptions.OnlyOnFaulted | TaskContinuationOptions.ExecuteSynchronously,
+            TaskScheduler.Default);
+        return false;
+    }
+
     /// <summary>
     /// Unblocks whatever the exchange is waiting on. Swallowing here rather than letting it out:
     /// this runs on the timer that fired the deadline, where a throw has nowhere to go.