The Register reports that cesium atomic clocks are on deck to be replaced with strontium models for higher accuracy. The strontiums (strontia?) are now good enough that you can’t use a “plain old atomic clock” to measure them.
According to Wikipedia, a cesium clock set accurately at midnight today will lose or gain about a second by New Year’s Day, 2038. So perhaps more accuracy might seem silly, until it’s noted that the same inaccuracy translates into about a foot per second at the speed of light.