We consider the rendezvous problem in an anonymous port-labelled connected simple graph. The objective is for two mobile agents to meet at some node of the graph without prior knowledge of the graph or the other agent’s position. An oracle, that knows the graph and the starting positions of the agents, helps the agents by placing identical pebbles, at most one per node at some of the nodes. We introduce faults by considering the presence of a single faulty node that may remove a pebble that is kept on the node, or may add a pebble where there was no pebble placed by the oracle. The position of the faulty node is unknown to the agents as well as the oracle. Our goal is to find an efficient rendezvous algorithm regardless of the number of pebbles placed by the oracle in the presence of a faulty node. For trees, we present an algorithm that uses \(O(D\log \Delta )\) pebbles and runs in time \(O(D \log \Delta )\) , where \(\Delta \) is the maximum node degree and D is the shortest path distance between the initial agent positions. We prove that our algorithm for trees is optimal in terms of time. Additionally, we study the problem in general graphs with the constraint that the initial agent positions are no more than distance three apart. We propose an algorithm using \(O(\log \Delta )\) pebbles with run time \(O(\log ^3 \Delta )\) .