We extend the Faulty RAM model by Finocchi and Italiano (2008) by adding a safe memory of arbitrary size $S$, and we then derive tradeoffs between the performance of resilient algorithmic techniques and the size of the safe memory. Let $δ$ and $α$ denote, respectively, the maximum amount of faults which can happen during the execution of an algorithm and the actual number of occurred faults, with $α\leq δ$. We propose a resilient algorithm for sorting $n$ entries which requires $O\left(n\log n+α(δ/S + \log S)\right)$ time and uses $Θ(S)$ safe memory words. Our algorithm outperforms previous resilient sorting algorithms which do not exploit the available safe memory and require $O\left(n\log n+ αδ\right)$ time. Finally, we exploit our sorting algorithm for deriving a resilient priority queue. Our implementation uses $Θ(S)$ safe memory words and $Θ(n)$ faulty memory words for storing $n$ keys, and requires $O\left(\log n + δ/S\right)$ amortized time for each insert and deletemin operation. Our resilient priority queue improves the $O\left(\log n + δ\right)$ amortized time required by the state of the art.