As Adrian suggested, you have to assign the result of a StringFormat
binding to a text control. Try this instead:
<Button>
<Button.Content>
<TextBlock>
<TextBlock.Text>
<MultiBinding StringFormat="{}{0},{1}">
<Binding Path="ActualWidth" RelativeSource="{RelativeSource Mode=FindAncestor,AncestorType={x:Type Button}}"/>
<Binding Path="ActualHeight" RelativeSource="{RelativeSource Mode=FindAncestor,AncestorType={x:Type Button}}"/>
</MultiBinding>
</TextBlock.Text>
</TextBlock>
</Button.Content>
</Button>