Let me start by saying I don't have a complete answer to your question but thought I would throw this out for discussion.
I welcome comments.
You can measure the performance difference of the blower between a system with a clean filter and a system with a dirty filter.The measurement will be precise for that one system given those specific filters at that point in time. But it would be hard to apply that to other systems. I don't know if that is of use to you. Also, that is only the blower. I have some thoughts on measuring the rest of the system but they are weak. See below.
In order to measure the blower performance you need some way of measuring the energy use of the system.
You could use an Amp meter (Fluke makes a good one) or an energy mgmt device like (e.g. TED http://www.theenergydetective.com/).
Once you have the energy mgmt device in place, run the system* with the old filter and note the energy use.
Replace the filter and take a new measurement.
Subtracting those two measurements will give you the energy wasted due to the blower.
That should be pretty accurate.
I ran a similar test trying to determine the performance difference with a barometric bypass open vs closed. I ran this test because I suspected the bypass was setup incorrectly and eating to much energy. My test proved my theory with real data.
However, you still need to account for the energy wasted from the heating system.
I have no great ideas here but will suggest the following two ideas as a better than nothing solution. I have little confidence of the accuracy of either of these but it might be better than nothing for a ballpark number and it opens up the discussion.
1. Use a ratio of the good filter to bad filter energy use and the system rated efficiency to the "bad filter" efficiency.
ex. Blower used 1000 watts with good filter and 1200 watts with bad filter. Furnace is 95% efficient (per mfg).
good filter energy / Bad filter efficiency = good system efficiency /bad system efficiency (BSE)
1000w x 1200 w = 95% x BSE or BSE = 88%
2. Calculate the additional time that the system has to run due to the inefficiency. Then calculate the fuel cost of that additional time (based on mfg data).
If the system is moving 800 cfm with a clean filter and we calculate the blower is only about 83% efficient (1000w/1200w), with a dirty filter then the system is pumping 664 cfm. To get the same total volume of air, the system with the dirty filter would need to run 20% more (664cfm x 120% = 800 cfm).
For calculation purposes, let's assume the cost to run the system is $1 per hr per mfg specs, and the system is running 10 hrs per day. It would thus cost an additional 2 hrs and thus $2 per day with the dirty filter.
Bonus option: Use both of the above methods and average them out.