When you consider that much effort (hopefully) goes into the design of other pages on the website, it's wrong to think that the search engine results page (SERP) should receive any less love.
There are several steps at which the zero SERP can be avoided or improved.
The first point of prevention is at the query formulation using as-you-type suggestions, did-you-mean corrections and auto corrections.
Then there's fallback strategies that widen the scope - these can be automatic or prompted by the user, but also tend to require that a wider context is still a useful context.
But some systems just inevitably end up with a zero SERP, so there has to be an effective strategy of dealing with that, and that has to be a double barrel strategy:
Provide clear communication - you must effectively communicate the zero result state and give advice on what they can do about it.
Provide a method of rectification - you must allow the user to reformulate and action the query.
Now you also have a great opportunity to educate the users on ways they might improve the way they formulate the query - see examples below
The worst thing you can do is leave the user feeling like they have to back pedal.
You always want users to feel like they are making progress and getting smarter.
You do this by
- allowing them to move forward with a reformulated search
- giving them an understanding of why there was no results
- explaining how close they were to actually finding results
- not making the user go back to start over again
- providing a mechanism for tweaking and exploring the query
- making them feel smarter by educating them in better ways to search effectively
So consider your example above of a zero SERP when searching for 'blue cars from 1986'. The important variables are the car, blue and 1986
It depends how close you are able to find alternative results. You might be able to suggest an alternate colour, or an alternate year, but it probably doesn't make sense to suggest a carrot instead of car.
If you can find results retaining one good variable, or within a reasonable 'distance' of the original terms (whether with one or two variables), then possible responses might look like: