Way to maintain same screen ratio on data projector as on Mac laptop

In giving presentations from my MacBook Pro on an Epson Data Projector (VGA connection), there is I have invariably found a decrease in the display dimensions. Initially only part of the previous screen area shows, but can be reset to fill the smaller screen. Normally — for example with a PowerPoint presentation — this smaller size is OK, but today I was accessing one of my websites directly from the laptop to illustrate its features in my seminar. The problem was that I had written the HTML/CSS so that the site was ‘responsive’, and one aspect of this responsiveness was that certain features were not shown at the viewport size of mobile devices. The viewport matched the dimensions I had set in the stylesheet for the iPad and I ended up not being able to demonstrate some of the features. Failing all else I could record and show a movie or temporarily change the stylesheet, but my question is whether there is any way of changing the resolution of the data projector display from my Mac.