Under the broader scope of optimization with explorable uncertainty, scheduling with explorable uncertainty (also known as scheduling with testing) has gained increasing attention. In scheduling with explorable uncertainty, the processing times of jobs can be potentially reduced through testing before processing. This paper studies perpetual scheduling problems within the framework of explorable uncertainty, focusing on two prominent examples: the bamboo trimming problem and the windows scheduling problem. In the bamboo trimming problem, we aim to establish a perpetual cutting schedule to minimize the maximum height of bamboos that grow at different rates. In the windows scheduling problem, we want to schedule pages on broadcasting channels such that the interval between any two consecutive broadcasts of each page does not exceed its specified window, while minimizing the total number of channels. For the bamboo trimming with explorable uncertainty problem, we present a 4-competitive algorithm for the online version and a 3.5-approximation algorithm for the offline version. For the windows scheduling with explorable uncertainty problem, we provide (3 + o(1))-competitive and (2 + o(1))-approximation algorithms for the online and offline versions, respectively.