<Button Name="btnFoo" Content="Foo" >
    <Button.ContextMenu Placement="Bottom" PlacementTarget="btnFoo">
        <MenuItem Header="Bar" />
    </Button.ContextMenu>
</Button>

gives me a runtime error 'UIElement' type does not have a public TypeConverter class

I also tried

<Button Name="btnFoo" Content="Foo" >
    <Button.ContextMenu Placement="Bottom" PlacementTarget="{Binding ElementName=btnFoo}">
        <MenuItem Header="Bar" />
    </Button.ContextMenu>
</Button>

and that put the ContextMenu in the top left corner of my screen, rather than at the Button

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