Federated Learning (FL) is envisaged to be a promising solution for collaboratively training a machine learning model while keeping the training data decentralized and private. Instead of sharing raw data to the central entity, the participating client devices share focused updates for aggregation to ensure global convergence of the model. Owing to the shortcomings of manually handcrafted neural network architectures, the research community is striving to develop Neural Architecture Search (NAS) approaches to automatically search for optimal networks that fit the clients’ data. Despite the inaccessibility of clients’ data in an FL setting, the federated NAS literature has recently witnessed great progress to apply these NAS techniques to an FL setting. However, one of the key bottlenecks of Federated Learning is the cost of communication between clients and the server, and the state-of-the-art federated NAS techniques search for networks with millions of parameters that require several rounds of communication to find the optimal weight parameters. Also, deploying a network having millions of parameters on edge devices (which are the typical participants in an FL process) is infeasible due to its computational limitations and increased latency. Thus, this work proposes Weight-Agnostic Federated Neural Architecture Search (WFNAS), a novel evolutionary framework to search for well-performing and minimally connected weight-agnostic network architectures in an FL setting. As the connectivity of the networks themselves is the solution, there is no need for weight training and hyperparameter tuning, reducing the communication overhead significantly. The experiments indicate a gain of nearly 40% for orthogonal (vertical FL) data distributions compared to local training. This work is the first federated NAS technique in the literature for vertical FL. Although the experiments are performed in a resource-constrained environment, the aim of this thesis is to show a new direction of research to the FL community.