A solution when using C++11:
I found this answer on StackOverflow: http://stackoverflow.com/a/38383389 It turns out C++11 has built-in functions for converting between various Unicode encodings.
#include "mex.h"
#include <algorithm>
#include <string>
#include <locale>
#include <codecvt>
...
std::string u8str = u8"µm²";
std::u16string u16str = std::wstring_convert< std::codecvt_utf8_utf16< char16_t >, char16_t >{}.from_bytes( u8str );
mwSize sz[ 2 ] = { 1, u16str.size() + 1 }; // +1 to include terminating null character
mxArray* mxstr = mxCreateCharArray( 2, sz );
std::copy( u16str.begin(), u16str.end() + 1, mxGetChars( mxstr )); // again +1 for terminating null character