Cesium runs fine on IE 11, but it is a little more finicky when it comes to video card/drivers support. What OS and video card are you using? Visit the vendor website and upgrade them to the latest official version and that will hopefully do the trick for you.
Cesium also works in the WebBrowser control, but you need to set some registry keys for your app in order to enable it. Here's some example code to do it in C# for instances (put this in your application startup code before anything else runs)
using (var software = Microsoft.Win32.Registry.CurrentUser.OpenSubKey("Software"))
using (var microsoft = software.OpenSubKey("Microsoft"))
using (var internetExplorer = microsoft.OpenSubKey("Internet Explorer"))
using (var main = internetExplorer.OpenSubKey("Main"))
using (var featureControl = main.OpenSubKey("FeatureControl", true))
{
using (var gpu = featureControl.CreateSubKey("FEATURE_GPU_RENDERING"))
{
gpu.SetValue(Path.GetFileName(Application.ExecutablePath), 1, Microsoft.Win32.RegistryValueKind.DWord);
}
}