Richard and Kaiwei: This process is actually pretty easy in SOLIDWORKS (as of version 2014). See the list below:
I created a basic coffee mug as an example here
Create a reference plane that cuts through the part. In this case, I estimated where the coffee cup would be "filled up" to.
After the plane is created, fire up the "Intersect" feature, and select the reference plane and the solid body.
Exclude the regions not needed, in most cases - those regions will be 1 and 3. The three listed regions here are all the possible bodies that can be created using the solid body and the reference plane I created.
Final step is to reference the above steps (from MI Ilmy) to calculate the volume of what's left (the internal volume of the coffee cup)