At one house, I use a silicone hot pad that looks like a waffle, and I cut it to fit my small saucepan. At the other, I use a "universal" silicone pot lid that fits in the bottom - it was part of a set, and too small for any of my pans.
Also, I bring the water to a boil with the devices in the pan, then turn the water down to barely simmering & set the timer. When the timer rings, I shut the heat off and let it cool. By controlling the boil, the parts just rest on the mat and don't move around.