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 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 devices. More recent results have yielded hybrid (SW/HW) security architectures comprised of a minimal set of features to support efficient and secure RA on low-end devices. All prior RA 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 the prover between successive RA instances. Second, it requires the prover to engage in a potentially expensive (in terms of time and energy) computation, which can be harmful for critical or real-time devices. To address these drawbacks, we introduce the concept of self-measurement where a prover device 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 ERASMUS : Efficient Remote Attestation via Self-Measurement for Unattended Settings, justify its features and evaluate its performance. In the process, we also define a new metric -- Quality of Attestation (QoA). We argue 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 towards handling attestation of multiple devices (i.e., a group or swarm) with high mobility.