Your quote: "the engine on my riding mower would begin sputtering at times"
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What do you mean by Sputtering? The internal condition of the engine is not likely to be the cause of this condition. Either fuel or ignition could cause this.

1. The Briggs magnetron ignition has been very reliable, but nevertheless, a failure could be occuring. A sparktest would help determne if the magnetron is going bad. Heat can affect this item. Run the test in a darken area when the condition is occuring. The color of the spark is not a factor as long as there is a steady spark. Another likely cause of misfire is the sparkplug may be breaking down. The correct heat range is important.

2. Check the fuel flow to the carburetor. Sometimes a small stone or debris finds a way into the fuel system and creates a partial block. If you have a gravity feed system, remove the fuel line from the carburetor and drain the fuel into a jar. Look for signs of dirt and water.

If your engine is equipped with the opposed twin, inspect the fuel line for cracks - especially around clamps. Some of the fuel lines on opposed twins are routed through the blower housing and some disassembly is required to inspect. The section of hose between the fuel filter and the carburetor often develops cracks due to the heat. Cracks allow air to be drawn into the fuel hose. The vacuum hose that operates the fuel pump on opposed twins frequently develops loose connections because clamps are not always used.

Fuel filters may require replacement. On a gravity system, the paper fuel filter may restrict fuel flow especially if the fuel tank is running low.

If the problem still exists after checking these ideas, the experts may offer more suggestions.

Thank you so much for the suggestions. I will let you know what I find. Thanks!

retired_again covered the bases very well. The only thing I would add is to just go ahead and replace the 15 y/o fuel lines,(including pump aspirator line if an op twin) clamps and filters. Also, you will want to know that the vent in the fuel cap is unobstructed.

"This only seemed to happen when then engine was hot."

If you try above suggestions and have no results, consider exhaust valve seat OR valve clearance. You really need to post the model number of your engine so we know what we are talking about.

Walt Conner