Both sides have had difficult starts to their Vanarama National League campaigns, winning once and losing four.
Leamington haven't tasted victory since the opening day of the season while Nuneaton have lost their last three games.
So this fixture at the LDJ Solicitors Stadium is looking particularly important going by the early league table, and Town midfielder Beswick hopes this can be the start of something good.
He said: "We know that nothing is won in August but by the same token you can still leave yourselves with a lot to do by making a slow start. That’s why we need to get ourselves on a run of results and Saturday would be a great time to start.
"It’s a local derby as well, so that will add extra spice to the occasion. A win would really kick-start us and give us a boost.
"It’s a different kind of test for us; with all due respect, the ambitions of Leamington are not the same as those of Harrogate Town, Kidderminster Harriers, York City and Brackley Town who we’ve faced so far this season.
He continued: "I know a few of their lads and it’s going to be another hard-fought game. They will come here solid and organised, but if we can break them down early on and get our noses in front, it will stand us in good stead to go on and get the result that we all crave.
"We need everyone pulling in the same direction and hopefully we’ll give the fans something to cheer about come the final whistle."