This paper describes two novel approaches to cost estimation of manufactured products where a data set of similar products have known manufactured costs. The methods use the notion of piecewise functions and are (1) clustering and (2) splines. Cost drivers are typically a mixture of categorical and numeric data which complicates cost estimation. Both clustering and splines approaches can accommodate this. Through four case studies, we compare our approaches with the often-used regression models. Our results show that clustering especially offers promise in improving the accuracy of cost estimation. While clustering and splines are slightly more complex to develop from both a user and a computational perspective, our approaches are packaged in an open-source software. This paper is the first known to adapt and apply these two well-known mathematical approaches to manufacturing cost estimation.