  Precision timing of millisecond pulsars in binary systems enables observers
to detect the relativistic Shapiro delay induced by space time curvature. When
favourably aligned, this enables constraints to be placed on the component
masses and system orientation. Here we present the results of timing campaigns
on seven binary millisecond pulsars observed with the 64-antenna MeerKAT radio
telescope that show evidence of Shapiro delay: PSRs~J0101$-$6422, J1101$-$6424,
J1125$-$6014, J1514$-$4946, J1614$-$2230, J1732$-$5049, and J1909$-$3744.
Evidence for Shapiro delay was found in all of the systems, and for three the
orientations and data quality enabled strong constraints on their orbital
inclinations and component masses. For PSRs~J1125$-$6014, J1614$-$2230 and
J1909$-$3744, we determined pulsar masses to be $M_{\rm p} = 1.68\pm 0.17 \,
{\rm M_{\odot}} $, $1.94\pm 0.03 \, {\rm M_{\odot}} $ and $1.45 \pm 0.03 \,
{\rm M_{\odot}}$, and companion masses to be $M_{\rm c} = 0.33\pm 0.02 \, {\rm
M_{\odot}} $, $0.495\pm 0.005 \, {\rm M_{\odot}} $ and $0.205 \pm 0.003 \, {\rm
M_{\odot}}$, respectively. This provides the first independent confirmation of
PSR~J1614$-$2230's mass, one of the highest known. The Shapiro delays measured
for PSRs~J0101$-$6422, J1101$-$6424, J1514$-$4946, and J1732$-$5049 were only
weak, and could not provide interesting component mass limits. Despite a large
number of millisecond pulsars being routinely timed, relatively few have
accurate masses via Shapiro delays. We use simulations to show that this is
expected, and provide a formula for observers to assess how accurately a pulsar
mass can be determined. We also discuss the observed correlation between pulsar
companion masses and spin period, and the anti-correlation between recycled
pulsar mass and their companion masses.
