Pinching antenna (PA) systems have recently emerged as a promising architecture for reconfigurable wireless communications by enabling flexible antenna placement along a dielectric waveguide. However, existing works typically assume perfect knowledge of user locations, which is impractical in real systems where location estimation errors are inevitable. In this paper, we investigate robust power allocation and antenna placement for PA systems under user location uncertainty. We consider both single-antenna and multi-antenna configurations, where the true user locations are unknown but lie within bounded uncertainty regions. For the single-antenna case, we adopt a worst-case robust design and leverage the S-procedure to transform the joint power allocation and antenna placement problem into a convex semidefinite program (SDP), ensuring that quality-of-service (QoS) constraints are satisfied for all possible user locations. For the multi-antenna case, we address the additional challenges arising from the superposition of channel components from multiple antennas by developing an efficient numerical procedure to evaluate the worst-case channel gain. Then, we derive a closed-form solution for optimal power allocation and develop a block coordinate descent algorithm to optimize antenna placement. Simulation results show that the proposed framework provides robustness to location uncertainty while achieving power consumption close to that of outage-based benchmark schemes.