Make Iterator function to return a null reference when an exception is thrown

I don't see a way to cause an Iterator to return an empty collection upon exception, if that is what you really want to do. If you do, you could stop using Iterator and Yield, and simply do

Public ReadOnly Property ProcessorIds As IEnumerable(Of String) Implements IHardwareIds.ProcessorIds
    Get
        Try
            Using s As New ManagementObjectSearcher(New SelectQuery("Win32_Processor"))
                Return s.Get().OfType(Of ManagementObject).Select(Function(o) o("ProcessorId").ToString())
            End Using
        Catch
            Return Enumerable.Empty(Of String)
        End Try
    End Get
End Property

Using LINQ without the Iterator actually allows you to remove the For Each and simplify the code.

(If you would rather return null, it's almost the same)

Public ReadOnly Property ProcessorIds As IEnumerable(Of String) Implements IHardwareIds.ProcessorIds
    Get
        Try
            Using s As New ManagementObjectSearcher(New SelectQuery("Win32_Processor"))
                Return s.Get().OfType(Of ManagementObject).Select(Function(o) o("ProcessorId").ToString())
            End Using
        Catch
            Return Nothing
        End Try
    End Get
End Property

however, returning null has a different feel that other Enumerable functions (such as Where, which returns an empty collection when the predicate is not satisfied by any element, as pointed out by @Anu6is).

You can also stop iteration upon the first exception. If Yield is never hit, your result is an empty collection. I think this is more in the spirit of Iterator.

Public ReadOnly Iterator Property ProcessorIds As IEnumerable(Of String) Implements IHardwareIds.ProcessorIds
    Get
        Try
            Using s As New ManagementObjectSearcher(New SelectQuery("Win32_Processor"))
                For Each mo In s.Get()
                    Yield mo("ProcessorId").ToString()
                Next
            End Using
        Catch
            Return ' or Exit Property
        End Try
    End Get
End Property

The C# analog is yield break; and it seems quite clean. See also this answer.