It depends on the project, but it is something I like to do. For responsive web site or web apps I think it is essential to prototype in the browser to show different screen sizes. I'm not a fan of producing 4-10 individual mockups for different screens sizes when I can show that in the browser. One of the bigger benefits for client work is the client sees exactly how it looks in whatever browser they are viewing it in. So there are no surprises when it launches.
Something that is essential to this process is the inspect element tool in your browser. For often than not I am inspecting and making changes in the browser before updating my HTML + CSS.
It depends on the project, but it is something I like to do. For responsive web site or web apps I think it is essential to prototype in the browser to show different screen sizes. I'm not a fan of producing 4-10 individual mockups for different screens sizes when I can show that in the browser. One of the bigger benefits for client work is the client sees exactly how it looks in whatever browser they are viewing it in. So there are no surprises when it launches.
Something that is essential to this process is the inspect element tool in your browser. For often than not I am inspecting and making changes in the browser before updating my HTML + CSS.