One warning first: this is going to be a bit literature-heavy, because I think that's what you're more or less explicitly ask for. You want something that you can read, understand and cite for your publication.
Firstly, my understanding is that a matched filter is the most common method for estimating signal-delay.
No. A matched filter can be used to effectively correlate a receive signal against a transmit signal shape. It's can but be a puzzle piece in a TDOA system.
Thus, what I'm looking for is how to calculate the variance in the signal-delay estimate using a matched filter as an estimator.
Again, the matched filter is not the delay estimator; think of it as a signal preconditioner!
Now, what you probably mean is that you use matched filters for the TX pulse shape and the RX pulse shape filter, and then, based on the post-filter signal, do a delay estimate.
I'd like to cite a paper,[1] :
which doesn't actually deal with matched filtering directly, as the TDoA system isn't able to define the pulse shape the transmitter uses; instead, it's about cross-correlation of the received signals at different positions.
The interesting point is that the defining entity (aside from the obvious $\frac{c}{f_\text{Nyquist}}$ limit) is the SNR of the received signal -- that's pretty obvious, if you think about it: The "certainty" with which the correlation of RX and TX signal has a maximum at the "right" position is reduced with increased SNR.
In previous work of the author, she uses in [2] that with AWGN assumption and cross-correlation (i.e. matched filter with a known TX signal)
$$\begin{align*}
\sigma^2_{\hat\tau}&=\frac{3}{8\pi^2}\,\frac{1+2\, \text{SNR}}{\text{SNR}^2}\, \frac {1}{T_o B^3}\text,\,\text{with}\\
\sigma^2_{\hat\tau}&: \text{Variance of the timing estimate}\\
T_o&: \text{Duration of observation, and}\\
B&: \text{bandwidth of the system.}
\end{align*}$$
Interesting here, aside from the $B^{-3}$ relationship of variance and bandwidth, is the cited paper (if you find it in fulltext available online for free; I have IEEExplore access, but I don't know about you...) [9], which pretty much should give you plenty of background to work with.
[1]Noha El Gemayel, Holger Jäkel, Friedrich K. Jondral: Error Analysis of a Low Cost TDoA Sensor Network, IEEE/ION Position, Location and Navigation Symposium 2014, Monterey, CA, USA, May 5-8, 2014
[2]Noha El Gemayel, Sebastian Koslowski, Friedrich K. Jondral:
A low cost TDOA Localization System: Setup, Challenges and Results,
,
10th Workshop on Positioning, Navigation and Communication 2013 (WPNC'13), Dresden, Germany, March 20-21, 2013
[9] G. Carter, Coherence and time delay estimation, Proceedings of the
IEEE, vol. 75, no. 2, pp. 236 – 255, Feb. 1987
