Similar to business or employment_related correspondence, military correspondence also has set standards for the closing (also called a “valediction”) which one should present before one’s signature. If your company conducts business with the military – or if you are applying for a job in the military – you should be aware that “Very Respectfully” (often abbreviated as “V/R”) is used in written and emailed correspondence between military members.
Formal communication is on the wane in modern life, but there are still times when it's the only correct way to reinforce a connection or convey information. If you're applying for a job, looking for a recommendation, or expanding your network, err on the side of formality. Don't let the slightly archaic feel of a formal business letter tempt you into using flowery, outdated language.