The stimulation of electromagnetic ion cyclotron (EMIC) waves by a magnetospheric compression is perhaps the closest thing to a controlled experiment that is currently possible in magnetospheric physics, in that one prominent factor that can increase wave growth acts at a well‐defined time. We present a detailed analysis of EMIC waves observed in the outer dayside magnetosphere by the four Magnetosphere Multiscale (MMS) spacecraft, Van Allen Probe A, and GOES 13 and by four very high latitude ground magnetometer stations in the western hemisphere before, during, and after a modest interplanetary shock on 14 December 2015. Analysis shows several features consistent with current theory, as well as some unexpected features. During the most intense MMS wave burst, which began ~ 1 min after the end of a brief magnetosheath incursion, independent transverse EMIC waves with orthogonal linear polarizations appeared simultaneously at all four spacecraft. He++ band EMIC waves were observed by MMS inside the magnetosphere, whereas almost all previous studies of He++ band EMIC waves observed them only in the magnetosheath and magnetopause boundary layers. Transverse EMIC waves also appeared at Van Allen Probe A and GOES 13 very near the times when the magnetic field compression reached their locations, indicating that the compression lowered the instability threshold to allow for EMIC wave generation throughout the outer dayside magnetosphere. The timing of the EMIC waves at both MMS and Van Allen Probe A was consistent with theoretical expectations for EMIC instabilities based on characteristics of the proton distributions observed by instruments on these spacecraft. Key Points MMS observed a burst of independent transverse EMIC waves with orthogonal linear polarizations following the shock Wave onsets at both MMS and Van Allen Probe A were consistent with theoretical expectations based on particle observations A rarely observed minimum in wave power at the gyrofrequency of He++ ions was present both before and after the shock