In addition to the best model architecture and hyperparameters, a full AutoML solution requires selecting appropriate hardware automatically. This can be framed as a multi-objective optimization problem: there is not a single best hardware configuration but a set of optimal ones achieving different trade-offs between cost and runtime. In practice, some choices may be overly costly or take days to train. To lift this burden, we adopt a multi-objective approach that selects and adapts the hardware configuration automatically alongside neural architectures and their hyperparameters. Our method builds on Hyperband and extends it in two ways. First, we replace the stopping rule used in Hyperband by a non-dominated sorting rule to preemptively stop unpromising configurations. Second, we leverage hyperparameter evaluations from related tasks via transfer learning by building a probabilistic estimate of the Pareto front that finds promising configurations more efficiently than random search. We show in extensive NAS and HPO experiments that both ingredients bring significant speed-ups and cost savings, with little to no impact on accuracy. In three benchmarks where hardware is selected in addition to hyperparameters, we obtain runtime and cost reductions of at least 5.8x and 8.8x, respectively. Furthermore, when applying our multi-objective method to the tuning of hyperparameters only, we obtain a 10\% improvement in runtime while maintaining the same accuracy on two popular NAS benchmarks.