Quantum Computing advances promote its incorporation into current computing systems. Because of this, a new type of system where quantum and classical computers coexist will be created. Using the Service-Oriented Computing model is possible to achieve this coexistence through hybrid (quantum-classical) service applications. As it occurs with current service applications, an important challenge is the placement of its services which consists of obtaining an optimal deployment of the application’s services along a computing distributed infrastructure. Currently, this problem can be resolved in classical applications with existing tools and methodologies. However, for this new type of hybrid (quantum-classical) service application, there is a lack of tools and techniques that consider the coexistence of both computing models and allow solving this placement problem. To address it, this paper presents an evaluation system to tackle the placement problem for (quantum-classical) service applications using model-checking techniques and utility theory. As a result, an optimal cost-performance deployment configuration is obtained by adapting and extending current techniques in quantitative verification and constraint solving.