Artificial intelligence explanations can make complex predictive models more comprehensible. To be effective, however, they should anticipate and mitigate possible misinterpretations, e.g., arising when users infer incorrect information that is not explicitly conveyed. To this end, we propose complementary explanations -- a novel method that pairs explanations to compensate for their respective limitations. A complementary explanation adds insights that clarify potential misconceptions stemming from the primary explanation while ensuring their coherency and avoiding redundancy. We introduce a framework for designing and evaluating complementary explanation pairs based on pertinent qualitative properties and quantitative metrics. Our approach allows to construct complementary explanations that minimise the chance of their misinterpretation.