You can calculate the required capacitor value like this:

The power supply charge Q (in Coulombs) required from the capacitor is Q = I * t, where I is current and t is time.

Also, Q = C * ΔV, where C is the capacitance and ΔV is the voltage drop as current flows out to the load.

So C * ΔV = Q = I * t and rearranging for C gives C = I*t/ΔV

For a 1A load and allowing no-more than 0.2v drop in voltage for no more than 0.05-sec:

C = 1 * 0.05/0.2 = 0.25F = 250,000uF