I will describe an ongoing work on calculating the vacuum tunneling rate in the presence of black holes. Previous calculations of the tunneling rate encountered difficulties due to the ambiguous choice of the vacuum state. In particular, the standard imaginary time approach results in an unsuppressed rate for small black holes, which can have far-reaching implications for the interplay of primordial black holes and Higgs vacuum decay. In this ongoing work, I will show an ongoing calculation of the tunneling rate for a simplified collapsing star geometry in the thin wall limit. With this approach, the vacuum is unambiguously chosen in the infinite past, as the metric there is asymptotically Minkowski. Our preliminary results show that for small black holes, the tunneling rate approaches the Minkowski rate, while for black holes of order the critical radius of the bubble - the exponential suppression is lowered.