It is paramount to ensure secure and trustworthy operations in Cyber-Physical Systems (CPSs), guaranteeing the integrity of sensing data, enabling access control, and safeguarding system-level operations. In this paper, we address trustworthy operations of next generation CPSs. Our idea is inspired by a trustworthy computing framework known as Proof-Carrying Code, in which foreign executables carry a model to prove that they have not been tampered with and they function as expected. In our context, we leverage the physical world--a channel that encapsulates properties impossible to tamper with remotely, such as proximity and causality--to create a challenge-response function. We call it Proof-Carrying Sensing and use it to help authenticate devices, collected data, and locations. A unique advantage of this approach, vis-à-vis traditional multi-factor or out-of-band authentication mechanisms, is that authentication proofs are embedded in sensor data and can be continuously validated over time and space without resorting to complicated cryptographic algorithms. This, in turn, makes it fit particularly well to CPSs where mobility and resource constraints are common.