Phase-change chalcogenide alloys, such as Ge_2Sb_2Te_5 (GST), have very different optical properties in their amorphous and crystalline phases. The fact that such alloys can be switched, optically or electrically, between such phases rapidly and repeatedly means that they have much potential for applications as tunable photonic devices. Here we incorporate chalcogenide phase-change films into a metal-dielectric-metal metamaterial electromagnetic absorber structure and design absorbers and modulators for operation at technologically important near-infrared wavelengths, specifically 1550 nm. Our design not only exhibits excellent performance (e.g. a modulation depth of ~77% and an extinction ratio of ~20 dB) but also includes a suitable means for protecting the GST layer from environmental oxidation and is well-suited, as confirmed by electro-thermal and phase-transformation simulations, to in situ electrical switching. We also present a systematic study of design optimization, including the effects of expected manufacturing tolerances on device performance and, by means of a sensitivity analysis, identify the most critical design parameters.