We get this call a lot from new Model A owners so here are some helpful hints for them but the could apply to other non pressure systems as well.
You put more fluid in the system than it needs.
Most people fill a tank to its opening (the neck). In radiators however the natural level may be lower than you think. In a 3 gallon system at rest, the fluid level is typically 3/4" about the tubes that enter the top header. This means that almost a 1/2 gallon of coolant is "extra" which is likely to be expelled when initially driving. When it finds that natural level it will stop.
You have clogged tubes in your radiator
If the coolant cannot get through the tubes because they are clogged with debris e.g. rust, scale etc. then the fluid becomes restrictive and will "back up" find the overflow and exit the system. Lose enough coolant and you may overheat.
Henry Ford began making round tubes in to oval tubes in 1930 because the tub geometry lends itself to better heat exchange. Today we make elliptical or flat tubes and while we have fewer tubes their elliptical shape has 2.93 times the contact area and the same volumetric throughput.
You're driving faster that the production year
People forget that the roads and tires and suspensions of the antique cars they drive limited their speed and that limited the rpm which drives the water pump. Speed restrictions when posted were usually 35 miles per hour and this is how fast most cars traveled.
In June, 1925 Lyle Sign Post, the chairman of the Maryland State Roads Commission, John Mackall, "advises substitution of the maximum speed limit with a minimum speed limit, to speed up traffic. Mackall also suggested slow-moving vehicles be barred from main streets during peak hours".
You installed an overzealous water pump
For a time manufacturers of Model A water pump reproduction were selling pumps with impeller designs that sent the fluid through the system faster than the tubes could permit. They sold the pump with a photocopied image recommending the new purchaser grind down the impeller as much as 1/3" to slow the flow to prevent fluid loss.
Your radiator was repaired and may not have had the baffle re-installed
Les Andrews wrote about this and it seems to have caused a panic among some owners. Baffles serve to knock down and diffuse coolant as it enters the tank and prevent it from "percolating" up to the open tube found in non pressure systems. We use the 1930 design bulletin as a template for our Model A baffles.
Beyond the Baffle
People have pinched the overflow or placed a roofing nail in the tube to prevent loss. These tricks will restrict the coolant's exit but be certain that the overflow tube does not become restrictive or you will have a pressure bomb on your hands.
We can also send out cones and discs to prevent further fluid loss. These simple fixes are non invasive and can be press fit to create a skirt that knocks down the fluid.
One-way pressure systems
Pressure in the auto came around in the late 30's. We have mild pressure systems for non pressure cars that are one-way and they are discreet. They simply keep the fluid from escaping or delaying the escape to the street.
Mild pressure is ~4psi so as not to tax or damage the rest of the system and because in most cases yo udo not need excessive pressure. Flatheads we recommend no higher than 7psi.
Pressure systems with recovery tank
We also place dummy neck for mascots and caps and locate a modern filler neck on the rear of a tank. This system expels fluid due to thermal expansion and/or overcapacity in to a tank and, when things cool down, a secondary action vacuums that coolant back into the radiator. You have a perpetual reserve of 1.3 pints of fluid in the system.
These are helpful for peace of mind and help with safety compliance in both hill climb and speed trial events.