Order of magnitude variability has been observed in the blazar sub-class of Active Galactic Nuclei on minute timescales. These high-energy flares are often difficult to explain with shock acceleration models due to the small size of the inferred emitting region, with recent particle-in-cell (PIC) simulations showing that magnetic reconnection is a promising alternative mechanism. Here, we present a macroscopic emission model physically motivated by PIC simulations, where the energy for particle acceleration originates from the reconnecting magnetic field. We track the radial growth and relative velocity of a reconnecting plasmoid, modelling particle acceleration and radiative losses from synchrotron and synchrotron self-Compton (SSC) emission. To test the viability of magnetic reconnection as the mechanism behind rapid blazar flares we simultaneously fit our model to the observed light-curve and SED from the 2016 TeV flare of BL Lacertae. We find generally that, without considering external photons, reconnecting plasmoids are unable to produce Compton-dominant TeV flares and so cannot reproduce the observations due to overproduction of synchrotron emission. Additionally, problematically large plasmoids, comparable in size to the entire jet radius, are required to emit sufficient SSC gamma-rays to be observable. However, our plasmoid model can reproduce the rapid TeV lightcurve of the flare, demonstrating that reconnection is able to produce rapid, powerful TeV flares on observed timescales. We conclude that while reconnection can produce SSC flares on the correct timescales, the primary source of TeV emission cannot be SSC and the size of plasmoids required may be implausibly large.