I used this syntax as I found online but it throws an error:
xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
<!-- Cool comment -->
xmlns:System="clr-namespace:System;assembly=mscorlib"
'Name cannot begin with the '<' character, hexadecimal value 0x3C. Line 4, position 5.' XML is not valid.
I assume those XAML namespace declarations are in the parent tag of your control? You can't put comments inside of another tag. Other than that, the syntax you're using is correct.
<UserControl xmlns="...">
<!-- Here's a valid comment. Notice it's outside the <UserControl> tag's braces -->
[..snip..]
</UserControl>