Determining potential protease sites within a recombinant protein
LC-MS is certainly quantitative and will give you a definitive answer, but it is costly and requires access to such a machine.

I presume you're analyzing your protein based on western blotting.

The first thing you should always do is verify your DNA sequence is coding for the protein product you want. Once you're sure of this, the western blot will give you an indication as to where your protein is (approximately) being cleaved. Say you protein has a predicted size of 40 kDa and you see a band at 20 kDa, then your cleavage is somewhere in the middle of your sequence. There are a TON of proteases that could be potentially cleaving your peptide and you need to have a hypothesis as to what that could be. Your peptide could be cleaved by an endopeptidase (cutting within), or a carboxypeptidase (C-terminal cleavage) or an aminopeptidase (N-termainal cleavage). To go back to the 20/40 kDa example, it could be your peptide was cleaved N-terminally o C-terminally down to a size of 20 kDa, or that it was literally cleaved in the middle by an endopeptidase.

Something you may consider is the use of a general protease inhibitor cocktail (Roche makes a really good tablet product called Complete and Complete mini tab). These mixes have a bunch of general protease inhibitors which will stop most cleavage events. If you still see cleavage after using an inhibitor cocktail, you can reasonably expect that you are not inhibiting the protease with the tablet (thus narrowing down your search) and then you can better comb through Expasy's PepCutter data. You should also do a literature search to see what has been reported about your peptide or motif.