You can't calculate the cognitive memory load of an interface, but you can calculate (estimate) the cognitive memory load of performing a particular task using an interface.
I don't have extensive knowledge of the "state of the art" when it comes to cognitive modeling, but I have done some GOMS modeling in the past. The general technique is to break down the task into basic steps (i.e., "keystroke-level" tasks), such as "point mouse at item on screen", "read value", "remember value", "type a character", etc., assign estimated times (from the literature) to each step, then add them up to get an estimate for the time to complete the task.
Since you're interested in memory in particular, you can just examine the steps that involve memory. Examples include "recall X chunks* of data from long-term memory", "recall X chunks of data from short-term memory", "store X chunks of data in working (short-term) memory", etc.
Once you've done this, there are several analyses you could do. Examples:
How many memory operations are required to perform this task?
How many memory overloads are likely to occur? Does the user ever need to accumulate more then 5 chunks of data in working memory to perform the task? If so, how often?
How much time must be spent on memory operations? A very rough time estimate would be 1.2 seconds per memory operation per chunk. So, accessing 3 chunks of data from long-term memory would require 3.6 seconds. Same with working memory.
*Note: "chunk" is really just a fancy way of saying "thing", as in "people can remember 7 plus or minus 2 things". The point is that each chunk takes up one "slot" in your memory store, so you might be able to remember a 10-digit phone number because you are able to process the first three numbers (the area code) as a single "chunk".
You might find this link helpful: Keystroke-Level Model