Most models of mutualism stabilize cooperative species interactions by putting non-cooperating individuals at a selective disadvantage, which should eliminate genetic variation in partner quality --- yet empirical studies often find such variation. One explanation for this paradox is that mutualisms are mediated not only by assessment of partner quality, but also by partner signals independent of quality. Here, we examine a model of host-symbiont coevolution in which host recognition of symbiont signals and ability to sanction non-cooperative symbionts are determined by alleles at independent loci, as are symbionts' expression of signals and cooperation. This model has unstable equilibria at which variation in interaction outcomes is maintained, even as mutualism persists; and coevolution of host recognition and symbiont signalling is modulated by coevolution of sanctions and cooperation. Individual-based simulations incorporating population structure show that, compared to simpler models, the dual-system model promotes greater local and among-population variation in hosts and maintains among-population variation in symbionts. The dual systems of sanctions and partner recognition also converge toward conditions similar to economic models of symbiosis in which hosts offering the right incentives to potential symbionts can initiate symbiosis without screening for partner quality. Our results reinforce the notion that studies of mutualism must consider communication between partner species as well as the exchange of benefits.