Instead of removing the whole plant, harvest all tomatoes of good size and place them in paper bags in a cool location. Place the tomatoes in a single layer in the bags. Tomatoes stacked on top of each other are more likely to be damaged. Check the bags regularly and remove fruit as it ripens. When calcium reaches low levels in the tomato, the fruit simply dies back at the bottom leaving the characteristic black or brown spot.
Calcium is present in most soils in adequate amounts.
The problem is that the plant cannot absorb enough calcium through its roots because of dry soil conditions. That's because calcium is taken up by the roots along with water. If, for some reason, water uptake is restricted, calcium uptake will stop. Have your soil tested to make sure you have enough calcium in the soil. If calcium levels are adequate, the most important control measure is to maintain optimum soil moisture.