Application services depend on the network to guarantee reliability, which is critical for safety and correct operation. Time-Sensitive Networking is a technology for reliable real-time communication of time-sensitive applications. While many schedulers exist that provide reliability for wired Time-Sensitive Networks (TSN) with the assumption of deterministic packet delays, scheduling for wireless TSN with uncertain packet delays has received significantly less attention. This work leverages the methodology of Robust Optimization (RO) to propose a robust scheduling approach that ensures provable reliability for both wired and wireless TSN. An uncertainty set defines the range of possible values, ensuring that the schedule remains feasible under all possible realizations within this set. As uncertainty sets are a key component in RO, we introduce methods to compute boxed and polytope uncertainty sets containing possible packet delays based on a set of given reliability requirements. A scheduler is deemed robust if it satisfies the given reliability constraints for all possible packet delays within the computed uncertainty set. Although robustness can be achieved through strict isolation and conservative filtering of packets, we demonstrate that several limitations prevent known robust schedulers from fully exploiting arbitrary uncertainty set shapes. As certain problem instances are unsolvable using simple boxed uncertainty sets, we indicate the need for schedulers that can utilize complex shapes of uncertainty sets rather than boxes. In response to this challenge, we introduce Uncertain No-Wait Packet Scheduling (UNWPS), a scheduler capable of computing robust schedules, and prove that UNWPS is robust against arbitrary upper-bounded boxed and polytope uncertainty sets. We assess the influence of uncertainty sets on the quality of the resulting UNWPS schedules, compare their performances to the performance of other robust scheduling approaches across various exemplary TSN networks and message stream configurations and carry out simulations conducted using the DetCom simulation framework to validate the robustness of UNWPS empirically.