When the user clicks the Verify button on the welcome page and a URI is generated, I would like the JavaScript to call the code that holds the WebView control to have the URI saved. 

This will save the user the trouble of having to copy the URI, open up the settings flyout, and paste in the new URI.

If you use the WebView's Navigate method then you must specify the list of URIs that are allowed to call the ScriptNotify event handler. 

If you use the WebView's NavigateToString method then the list of URIs is not necessary.

List<Uri> lstAllowedUris = new List<Uri>(); 
lstAllowedUris.Add(new Uri("http://apps.dovico.net")); 
wvBrowser.AllowedScriptNotifyUris = lstAllowedUris;

In reality, based on my testing, even if you specify a URI to a particular page, any page within that domain can call the event handler. 

The AllowedScriptNotifyUris property is really a list of allowed domains who's pages are allowed to call the ScriptNotify event handler.

public MainPage() 
{
// Only allow the following domain's pages to call our ScriptNotify 
// event handler 
List<Uri> lstAllowedUris = new List<Uri>(); 
lstAllowedUris.Add(new Uri("http://apps.dovico.net")); 
wvBrowser.AllowedScriptNotifyUris = lstAllowedUris; 

// Attach our ScriptNotify event handler 
wvBrowser.ScriptNotify += wvBrowser_ScriptNotify;
}

void wvBrowser_ScriptNotify(object sender, NotifyEventArgs e) 
{
// The string received from the JavaScript code can be found 
// in e.Value
}

// We have a couple of checks to make sure the 'external' 
// object and 'notify' method exist before we try using them 
// because our project is a web application and might not be 
// running in a WebView control (the checks prevent 
// JavaScript errors if the method doesn't exist) 
if ((typeof (window.external) !== "undefined") && 
(typeof (window.external.notify) !== "undefined")) 
{
window.external.notify(sURI);
}