WebbPSF: The program WebbPSF models Point Spread Functions for the James Webb Space Telescope, using predicted wavefronts based on the optical requirements and error budgets for the telescope and instruments. WebbPSF can produce monochromatic and broadband PSFs for all instruments in direct imaging and coronagraphic modes; spectroscopic modes are not yet supported.
Astronomer's Proposal Tool (APT): APT is the operational tool for writing HST proposals and it is being modified to also write JWST proposals. You can download the current operational version of APT here and look at the current draft version for JWST by clicking on File>New>New JWST Proposal. Note that at this point the observation templates generally reflect what has been developed for the on board scripts and not necessarily all planned functionality.
JWST Prototype ETC: This JWST prototype Exposure Time Calculator (ETC) is a web-based application that assists users in exploring JWST's science capabilities. The ETC calculates Signal-To-Noise Ratio (SNR) for a given exposure time for JWST's science instruments.
Simulating Slitless Spectroscopy with NIRISS: Software is available to model wide-field slitless spectroscopic (WFSS) observations with NIRISS and to extract and calibrate the resulting spectra. The tools employed are the aXe package of programs, which was developed to support slitless spectroscopy with ACS and WFC2 on the Hubble Space Telescope, and Source Extractor, which builds a catalog of objects from an astronomical image.