The paper addresses the relevant issue of ensuring the reliability of solving large scientific and applied problems in computing environments that integrate Grid and cloud computing. The main reliability parameter is the probability of successful problem-solving in a computing environment with the following specified quality criteria: efficiency of the allocated resources use, and time, deadline or cost of executing jobs. We propose a new technology for testing and evaluating the reliability of functioning of problem-oriented heterogeneous distributed computing environments. It integrates models, representing different layers of knowledge about the environments, and special tools that automate a study of these environments. Applying such technology provides an increase in the reliability and efficiency of heterogeneous distributed computing environments by parametric adjusting of local resources managers installed in the environment nodes. Their adjustment is implemented on the base of the results of testing and evaluating obtained with the use of complex (conceptual, simulation, and semi-natural) modeling and meta-monitoring of computational resources.