A
SMS text does not allow for text formatting. It is pure text only.
Email does text formatting if you have HTML or RTL formatting turned on.
That said, many email apps for your phone will probably not have that feature since "selecting the text and pressing the underline button" is not easy to do on a phone.
Back in the days before formatted text, we would use special chars to start and top the "formatting":
_text_ for underlines
*text* for bold
/text/ for italics, maybe.
Many computer programs still understand this and translate it automatically.
I have not tried it with phone apps.
Gmail and Aqua mail have it.