  Many transient and variable sources detected at multiple wavelengths are also
observed to vary at radio frequencies. However, these samples are typically
biased towards sources that are initially detected in wide-field optical, X-ray
or gamma-ray surveys. Many sources that are insufficiently bright at higher
frequencies are therefore missed, leading to potential gaps in our knowledge of
these sources and missing populations that are not detectable in optical,
X-rays or gamma-rays. Taking advantage of new state-of-the-art radio facilities
that provide high quality wide-field images with fast survey speeds, we can now
conduct unbiased surveys for transient and variable sources at radio
frequencies. In this paper, we present an unbiased survey using observations
obtained by MeerKAT, a mid-frequency ($\sim$1.4 GHz) radio array in South
Africa's Karoo Desert. The observations used were obtained as part of a weekly
monitoring campaign for X-ray binaries (XRBs) and we focus on the field of MAXI
J1820+070. We develop methods to optimally filter transient and variable
candidates that can be directly applied to other datasets. In addition to MAXI
J1820+070, we identify four likely active galactic nuclei, one source that
could be a Galactic source (pulsar or quiescent X-ray binary) or an AGN, and
one variable pulsar. No transient sources, defined as being undetected in deep
images, were identified leading to a transient surface density of
$<3.7\times10^{-2}$ deg$^{-2}$ at a sensitivity of 1 mJy on timescales of one
week at 1.4 GHz.
