There's no built-in automated way to interrupt a calculation, quit Mathematica, then resume the calculation at a later time.
It is however often possible to implement something like this yourself. I have done this several times when the problem was simple enough to allow it. But it needs to be done manually. You need to store the state of the calculation explicitly in some variable. You can then Export this variable to the MX format, quit Mathematica, then reload the variable later in a different session.
Caveat: In version 10 MX files are not portable between 32 bit and 64 bit platforms, but they are portable between different operating systems. In Mathematica 9 they are not even portable between different operating systems.
There are other formats than MX that support general Mathematica expressions.There are other formats than MX that support general Mathematica expressions.