While the subject of engineering mathematics, as the name suggests, blends both engineering and mathematics, some universities park the subject under ‘Computational Sciences’ as they see it as being “at the intersection of mathematics, computing, engineering and applied sciences”. Some ask for a graduation background in engineering while some others ask for a background in Mathematics, Physics, Computer Science or Engineering. Whatever the nomenclature, the discipline has great practical applications with opportunities to work either in research centres or the corporate sector, and will certainly involve great deal of mathematical analysis and computational capabilities. The emphasis on specific areas of work varies across universities.
Following is an indicative coverage of universities offering both Masters and PhD programmes in the subject. You should carry out further search based on what interests you.
The Dalhousie University offers both MSc and PhD in engineering mathematics “designed for students who have already completed an undergraduate program in Mathematics, Physics, Computer Science, or Engineering”. They have many current research projects.
If you are looking for studying anywhere in the European Union, you could consider a M.Sc. Engineering Mathematics and Computational Science, EU (http://www.mastersportal.eu/studies/111/engineering-mathematics-and-computational-science.html) or a M.Sc. Applied and Engineering Mathematics (http://www.mastersportal.eu/studies/32168/applied-and-engineering-mathematics.html). Incidentally, you could search more using the main URL.
In the USA, The University of Akron, Ohio’s Polytechnic University offers only a Ph.D. in Engineering Applied Mathematics.
The Purdue University calls it MS in Interdisciplinary Engineering and runs the programme under its College of Engineering, Mathematics and Science
The Stanford Institute for Computational & Mathematical Engineering offers a Computational and Mathematical Engineering MS Degree under The Institute for Computational and Mathematical Engineering (ICME). As they describe, “iCME designs state-of-the-art mathematical and computational models, methods, and algorithms for engineering and science applications. The program collaborates closely with engineers and scientists in academia and industry to develop improved computational approaches and advance disciplinary fields”.
The University of Canterbury offers a Master of Engineering Studies catering to “professional engineers seeking advanced technical training and is a taught master’s degree with no thesis requirement. The MEngSt is offered by the Departments of Chemical and Process Engineering, Civil and Natural Resources Engineering, Electrical and Computer Engineering, and Mechanical Engineering’ clearly underlining a focus on a “broad range of topics in their general area of expertise”.
The University of Oxford offers a variety of programmes under the rubric of Mathematical, Physical and Life Sciences.