  The James Webb Space Telescope (JWST), scheduled for launch in 2018, is the
successor to the Hubble Space Telescope (HST) but with a significantly larger
aperture (6.5 m) and advanced instrumentation focusing on infrared science
(0.6-28.0 $\mu$m ). In this paper we examine the potential for scientific
investigation of Titan using JWST, primarily with three of the four
instruments: NIRSpec, NIRCam and MIRI, noting that science with NIRISS will be
complementary. Five core scientific themes are identified: (i) surface (ii)
tropospheric clouds (iii) tropospheric gases (iv) stratospheric composition and
(v) stratospheric hazes. We discuss each theme in depth, including the
scientific purpose, capabilities and limitations of the instrument suite, and
suggested observing schemes. We pay particular attention to saturation, which
is a problem for all three instruments, but may be alleviated for NIRCam
through use of selecting small sub-arrays of the detectors - sufficient to
encompass Titan, but with significantly faster read-out times. We find that
JWST has very significant potential for advancing Titan science, with a
spectral resolution exceeding the Cassini instrument suite at near-infrared
wavelengths, and a spatial resolution exceeding HST at the same wavelengths. In
particular, JWST will be valuable for time-domain monitoring of Titan, given a
five to ten year expected lifetime for the observatory, for example monitoring
the seasonal appearance of clouds. JWST observations in the post-Cassini period
will complement those of other large facilities such as HST, ALMA, SOFIA and
next-generation ground-based telescopes (TMT, GMT, EELT).
