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Really, if you evaluate Style["/", Underlined] or type / and set the font of the character to be underlined through Format|Font..., you get $/$, not $\underline{/}$.
What I want to do is to underline a hyperlink, but...
enter image description here
the output is ugly. Note, that line has a gap before ".com".
This is not the problem of 'Courier New' only. I think this behavior caused because /, //, ., etc. are operators.

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You can use UnderBar instead of Style[...,Underlined]:

Hyperlink[UnderBar[#], #] &@ "http://www.wolfram.com/Sine.html" 

enter image description here

Note: The issue you observe is mentioned in the docs Underlined >> Possible Issues:

Underlined will recursively affect all elements of an expression

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  • $\begingroup$ Thank you. I couldn't guess to use under-bar operator, instead I sticked to text formatting. $\endgroup$ – Dan Oak Apr 23 '15 at 12:20
  • $\begingroup$ @Danylo, my pleasure. Thank you for the accept. $\endgroup$ – kglr Apr 23 '15 at 12:21

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