Dimensional analysis is your friend. A Farad is a coulomb per volt. An Ampere is a coulomb per second.
To figure how much capacitance is needed, you've got to know how much charge (coulombs) must be delivered, and how much the voltage is allowed to sag while delivering the charge.
To figure the charge, multiply amperage times seconds to get coulombs. If it needs 200mA for 2 seconds, that would be 200mA*2s * 1A/1000mA = 0.4 coulombs
Suppose the capacitor starts at 12V, and is allowed to sag down to 7V before your regulator drops out (you'll need to verify the allowable lower limit on your voltage; you haven't given that). That would mean the voltage can sag 5V while the capacitor delivers 0.4 coulombs. The required capacitance is 0.4coulombs/5V = 0.08F
To guarantee things work right, you'll want to analyze the worst case. Look at the longest time required for saving data, highest current draw during that time, lowest voltage that triggers your "save everything, we're going down" routine, and highest input voltage on your regulator that could cause problems due to dropout issues. Add a safety factor, and look at the tolerances on your capacitors.