Remote attestation (RA) is a popular means of detecting malware in embedded and IoT devices. RA is usually realized as an interactive protocol, whereby a trusted party ( verifier ) measures software integrity of a potentially compromised remote device ( prover) . Early work focused on purely software-based and fully hardware-based techniques, neither of which is ideal for low-end embedded devices. More recent results yielded hybrid (SW/HW) architectures with a minimal set of features to support efficient and secure RA on low-end devices. All prior techniques require on-demand operation , i.e., RA is performed in real time . We identify some drawbacks of this general approach in the context of unattended devices: First, it fails to detect mobile malware that enters and leaves prover between successive RA instances. Second, it requires prover to engage in a potentially expensive (in terms of time and energy) computation, which can be harmful for mission-critical or real-time devices. To address these drawbacks, we introduce the concept of self-measurement , whereby prover periodically and securely measures and records its own software state, based on a pre-established schedule. A (possibly untrusted) verifier occasionally collects and verifies these measurements. We present the design of a concrete technique, called Efficient Remote Attestation via Self-Measurement for Unattended Settings, (ERASMUS), justify its features and evaluate its performance. In the process, we also define a new metric, Quality of Attestation (QoA). We believe that ERASMUS is well suited for time-sensitive and/or safety-critical applications that are not served well by on-demand RA. Finally, we show that ERASMUS is a promising stepping stone toward handling attestation of multiple devices (i.e., a group or swarm) with high mobility.