Are there any hacks to archive and preserve a site for presentation purposes

Let's say for example you developed a website and would like to present it in your portfolio.

It was built for a company, so it will most certainly change over time. So obviously, linking to the active domain is not a solution.

I know services like the wayback machine exist. However, this doesn't appear to preserve sites completely.

Is there any way to neatly package and present a website demo without dealing with decay? (I suppose some decay is unavoidable with advancements and changes to the web and clients)