Automated platforms which support users in finding a mutually beneficial match, such as online dating and job recruitment sites, are becoming increasingly popular. These platforms often include recommender systems that assist users in finding a suitable match. While recommender systems which provide explanations for their recommendations have shown many benefits, explanation methods have yet to be adapted and tested in recommending suitable matches. In this paper, we introduce and extensively evaluate the use of "reciprocal explanations" -- explanations which provide reasoning as to why both parties are expected to benefit from the match. Through an extensive empirical evaluation, in both simulated and real-world dating platforms with 287 human participants, we find that when the acceptance of a recommendation involves a significant cost (e.g., monetary or emotional), reciprocal explanations outperform standard explanation methods which consider the recommendation receiver alone. However, contrary to what one may expect, when the cost of accepting a recommendation is negligible, reciprocal explanations are shown to be less effective than the traditional explanation methods.