I found these three workarounds, on top of the other answers:
1) Simple Workaround (using package and a different command)
As a workaround I am using the \Checkmark from the bbding package as from this answer https://tex.stackexchange.com/a/10194/1871. Unfortunately it is not exactly equal to the checkmark from amsfonts.

\documentclass{article}
\usepackage{bbding} % for the \Checkmark command
\usepackage{unicode-math}
\usepackage{fontspec}
\setmainfont{Cambria}
\setsansfont{Calibri}
\setmathfont{Cambria Math}
\begin{document}
$a + b$
\begin{itemize}
\item[\Checkmark] a
\item[\Checkmark] b
\item[\Checkmark] c
\end{itemize}
\end{document}
2) "MSWord"-consistent answer (use Wingdings font)
Itemize in MSWord use the Wingdings font for check marks, therefore this gives a consistent look (look for David's answer for the rest of the code).
\newfontfamily\wingdingsfont{Wingdings}
\newcommand\wingdings[1]{{\wingdingsfont\symbol{#1}}}
\AtBeginDocument{\renewcommand\checkmark{\wingdings{252}}}

3) Poor's man (use existing unicode glyphs within Cambria)
Another pure-Cambria (but horrible) workaround is to use a different symbol for checkmark (which naturally looks more like a square root):
\begin{itemize}
\item[$⎷$] a
\item[√] b
\item[\checkmark] c (for comparison) %using solution #2
\end{itemize}

\usepackage{fontawesome}and then\item[\faOk]? The package relies onfontspec(and requiresXeTeXorLuaTeX), so there should be no incompatibility. – jon Apr 14 '13 at 05:49\faOklooks quite different than the expected output of\checkmark. – alfC Apr 14 '13 at 06:06unicode-mathpeople since it is still, I think, an experimental package. – jon Apr 14 '13 at 06:22unicode-math, I had other problems with it, for example, when using Cambria in the documentEvincePDF viewer refuses to print! – alfC Apr 14 '13 at 07:14