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Evaluation can be defined as a process of determining the significance of a research output. This is usually done by devising a well-structured study on this output using one or more evaluation measures in which a careful inspection is performed. This paper presents a review of evaluation techniques for Conversational Agents (CAs) and Natural Language Interfaces to Databases (NLIDBs). It then introduces the developed customized evaluation methodology for Conversation-Based Interface to Relational Databases (C-BIRDs). The evaluation methodology created has been divided into two groups of measures. The first is based on quantitative measures, including two measures: task success and dialogue length. The second group is based on a number of qualitative measures, including: prototype ease of use, naturalness of system responses, positive/negative emotion, appearance, text on screen, organization of information, and error message clarity. Then an elaboration is carried out on the devised methodology by adding a discussion and recommendations on the sample size, the experimental setup and the scaling in order to provide a comprehensive evaluation methodology for C-BIRDs. In conclusion the evaluation methodology created is better way for identifying the strengths and weaknesses of C-BIRDs in comparison to the usage of single measure evaluations.