Despite the growing popularity of GPGPU programming, there is not yet a portable and formally-specified barrier that one can use to synchronise across workgroups. Moreover, the occupancy-bound execution model of GPUs breaks assumptions inherent in traditional software execution barriers, exposing them to deadlock. We present an occupancy discovery protocol that dynamically discovers a safe estimate of the occupancy for a given GPU and kernel, allowing for a starvation-free (and hence, deadlock-free) interworkgroup barrier by restricting the number of workgroups according to this estimate. We implement this idea by adapting an existing, previously non-portable, GPU interworkgroup barrier to use OpenCL 2.0 atomic operations, and prove that the barrier meets its natural specification in terms of synchronisation. We assess the portability of our approach over eight GPUs spanning four vendors, comparing the performance of our method against alternative methods. Our key findings include: (1) the recall of our discovery protocol is nearly 100%; (2) runtime comparisons vary substantially across GPUs and applications; and (3) our method provides portable and safe inter-workgroup synchronisation across the applications we study.