In a globally competitive world, with diminishing profit margins and decreasing market shares, the cost of a project is one of the major criteria in decision making at the early stages of a building design process in the construction industry. To remain competitive in the market, it is crucial for companies to have an accurate estimate of their projects. Nevertheless, given that very little is known about the scope and details of the project, the conventional cost estimation methods tend to be slow and inaccurate. With the rise of computing power, there is now a tendency to use Machine Learning (ML)-based methods, such as Artificial Neural Networks (ANNs), for more accurate cost estimation that can remain reliable in face of insufficient details during the tendering phase. While the use of ANN for cost estimation has been abundantly investigated from the perspective of contractors, there are very limited studies on the development and application of ML-based methods for engineering consultancy firms. Given that the nature of products/services offered by consultancy firms is inherently different from that of contractors (i.e. they are more abstract and less material-based) and also given that the type and level of detail of the available data at the tendering stage is dissimilar, it is important to investigate the applicability of ML-based methods for cost estimation in consultancy firms. To this end, this paper presents an artificial neural network approach for the cost estimation of engineering services. In developing the model, first, the influential factors that affect the costs of engineering services are identified. Thereafter, a model is developed using the data of 132 projects. Subsequently, a heuristic method is developed to systematically improve and fine-tune the performance of the model. Eventually, the findings show that artificial neural networks (ANNs) can obtain a fairly accurate cost estimate, even with small datasets. In fact, the model proposed in this paper performed better than those proposed in other similar works. The model developed in this study showed a 14.5% improvement in the accuracy of the model, considering MAPE.