DoModalLoopStep.cs

        [DllImport("user32.dll", CharSet = CharSet.Auto, ExactSpelling = true)]
        private static extern int MsgWaitForMultipleObjectsEx(int nCount, IntPtr pHandles, int dwMilliseconds, int dwWakeMask, int dwFlags);

        private static Action _modalDoEvents;

        // WinForms doesn't have a proper modal loop outside ShowDialog
        // Sometimes we don't want ShowDialog, eg. for filter bar popups
        // There we want the popup to close if we click outside of it, which doesn't work with ShowDialog
        //
        // The replacement would be message pumping with Application.DoEvents and waiting for new messages
        // We can't use System.Thread.Thread.Sleep because this will not wake up when new messages arrive
        // The correct solution is to use MsgWaitForMultipleObjects(Ex) which is not exposed by WinForms
        //
        // This method is intended to be used like this:
        //   while(dlg.Visible)
        //     DoModalLoopStep();
        //
        public static void DoModalLoopStep()
        {
            if (_modalDoEvents == null)
            {
                var type = typeof(Application);
                var method = type.GetMethod("DoEventsModal", System.Reflection.BindingFlags.Static | System.Reflection.BindingFlags.NonPublic);
                _modalDoEvents = (Action)Delegate.CreateDelegate(typeof(Action), method);
            }

            // This previously used Application.DoEvents() but this causes problems in Excel: it pushes a message loop with "do events" reason,
            // causing Excel to intercept key input and redirect it to the main window, even though the containing message loop is modal.
            // The real PropertyGrid (mentioned below) uses Application.DoEventsModal() which works in Excel but is not public.
            // Since there is no other way to mimic a modal loop we'll just do the same and use reflection to invoke DoEventsModal.
            _modalDoEvents();

            // Flags used are:
            // - 0, IntPtr.Zero = we don't wait on any handles
            // - 250 ms timeout if no message arrives
            // - 255 = QS_ALLINPUT & ~QS_RAWINPUT
            // - 4 = MWMO_INPUTAVAILABLE
            //
            // The flags are derived from reflector by looking at PropertyGrid, which also shows popup controls
            // (System.Windows.Forms.PropertyGridInternal.PropertyGridView.DropDownHolder.DoModalLoop)
            //
            MsgWaitForMultipleObjectsEx(0, IntPtr.Zero, 250, 255, 4);
        }

WinForms has a DoModalLoop implementation which can be used like this to show a modal splash screen or popup without calling ShowDialog

popup.Show();
while (!exitModalLoop && popup.Visible)
    Utilities.DoModalLoopStep();

(where exitModalLoop is an optional additional variable to exit the loop without closing the popup)

To use it in a WPF application you may have to initialize the WinForms Application before the WPF application, at least thats what we're doing.