Large language models (LLMs) are increasingly attracting the attention of healthcare professionals for their potential to assist in diagnostic assessments, which could alleviate the strain on the healthcare system caused by a high patient load and a shortage of providers. For LLMs to be effective in supporting diagnostic assessments, it is essential that they closely replicate the standard diagnostic procedures used by clinicians. In this paper, we specifically examine the diagnostic assessment processes described in the Patient Health Questionnaire-9 (PHQ-9) for major depressive disorder (MDD) and the Generalized Anxiety Disorder-7 (GAD-7) questionnaire for generalized anxiety disorder (GAD). We investigate various prompting and fine-tuning techniques to guide both proprietary and open-source LLMs in adhering to these processes, and we evaluate the agreement between LLM-generated diagnostic outcomes and expert-validated ground truth. For fine-tuning, we utilize the Mentalllama and Llama models, while for prompting, we experiment with proprietary models like GPT-3.5 and GPT-4o, as well as open-source models such as llama-3.1-8b and mixtral-8x7b.