Large Language Models have been recently exploited as judges for complex natural language processing tasks, such as Q&A. The basic idea is to delegate to an LLM the assessment of the "quality" of the output provided by an automated technique for tasks for which: (i) quantitative metrics would only tell part of the story, and; (ii) a large-scale human-based evaluation would be too expensive. LLMs-as-a-judge, if proven effective for a specific task, can also unlock new possibilities for automation, with several LLMs proposing a solution for a given instance of the task and others judging and deciding what is the best output to show the user. We study the effectiveness of LLMs-as-a-judge for two code-related tasks, namely code generation and code summarization. The rationale for choosing these tasks is two-fold. First, quantitative metrics are usually not enough for the assessment of code summarizers/generators. For example, it is well documented that metrics such as BLEU are quite weak proxies for the quality of the generated summaries. Second, even state-of-the-art techniques still struggle with handling complex instances of these tasks, making them good candidates for benefiting from more advanced solutions envisioning collaboration among LLMs. For code generation, we check whether eight LLMs are able to judge the correctness of 1,405 Java methods and 1,281 Python functions generated by the same LLMs or implemented by humans. For code summarization, we compare the judgment of five LLMs to those provided by nine humans for ~1.2k summaries, related to both Java and Python functions. Our findings show that GPT-4-turbo is the best LLM in terms of judging capabilities for both tasks, with "smaller" LLMs featuring tens of billions parameters not being able to cope with judging tasks. However, even the best-performing LLM frequently misjudges the correctness of the code and summary quality.