What is the best way to demonstrate a small device on a bigger display?

I am doing a presentation for a responsive site which I and my team have been developing over the last weeks. We would like to avoid using slides and do a demo on a protector and demonstrate how the experience is using a phone.

One option would be to use the browser and have the developer tools open and show the device frame this way.

That way I would not need an phone even, but this is just an emulator. The browser does not use the same engine that the iPhone (in my example) is using.

So I'm trying to find an alternative because there are some inconsistencies among the browser and the phone on the prototype we have now developed and therefore looking for a way using the mobile phone during the presentation.

Looking forward for any help, tips or ideas.