Return an empty IEnumerator

This is simple in C# 2:

public IEnumerator GetEnumerator()
{
    yield break;
}

You need the yield break statement to force the compiler to treat it as an iterator block.

This will be less efficient than a "custom" empty iterator, but it's simpler code...

There is an extra function in the framework:

public static class Enumerable
{
    public static IEnumerable<TResult> Empty<TResult>();
}

Using this you can write:

var emptyEnumerable = Enumerable.Empty<int>();
var emptyEnumerator = Enumerable.Empty<int>().GetEnumerator();

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