I would do the following. First, let assume that the buffer is a week acid (base will be similar).
Then to the right side from the buffer will be the equivalence point where concentration of H+ is equal to added OH- from strong base. That part of the chart almost vertical and represent the drastic change in pH. So, to reach this point you have to add the equivalent amount of base.
On the left side it is not so clean, if we add strong acid and assume(not exactly) that all new H+ react with conjugate base A- pushing base ions back to weak acid (or A- + H+ --> HA) then there will be no more acidic buffer capacity. Which gives us an estimation from the left side. Add as much H= as you have [A-].
To be exact we have to define what is the "significant change" and solve the equation where the first derivative of equilibrium is equal to the value for "significant change".
Is there are any other ways?