I don't think there's a reliable way of doing this, because there a just too many factors with managed code (any, not just MVC):
- garbage collection
- connection pooling
- etc...
But one that you can't avoid at all and is very undefinable: your data. Let's say, you're pulling a list of some records that may be this or that long with this or that much properties, with strings of whatever length... You won't be able to reliably estimate memory consumption at all. Especially if users enter data which is probably 99.9% common to all applications in one way or another.
I'd suggest something @mare suggested. Stress test it yourself or get someone do it for you. There are companies doing it against payment.
You can as well do the trial-and-error approach. Launch your app and add resources as it runs. :) But this depends largely on how critical this solution is.