As astronomy enters the petascale data era, astronomers are faced with new challenges relating to storage, access and management of data. A shift from the traditional approach of combining data and analysis at the desktop to the use of remote services, pushing the computation to the data, is now underway. In the field of cosmological gravitational microlensing, future synoptic all--sky surveys are expected to bring the number of multiply imaged quasars from the few tens that are currently known to a few thousands. This inflow of observational data, together with computationally demanding theoretical modelling via the production of microlensing magnification maps, requires a new approach. We present our technical solutions to supporting the GPU-Enabled, High Resolution cosmological MicroLensing parameter survey (GERLUMPH). This extensive dataset for cosmological microlensing modelling comprises over 70,000 individual magnification maps and ${\sim}10^6$ related results. We describe our approaches to hosting, organizing, and serving ${\sim}$30 Terabytes of data and metadata products. We present a set of online analysis tools developed with PHP, JavaScript and WebGL to support access and analysis of GELRUMPH data in a Web browser. We discuss our use of graphics processing units (GPUs) to accelerate data production, and we release the core of the GPU-D direct inverse ray--shooting code (Thompson et al., 2010; Astrophysics Source Code Library, record ascl:1403.001) used to generate the magnification maps. All of the GERLUMPH data and tools are available online from http://gerlumph.swin.edu.au . This project made use of gSTAR, the GPU Supercomputer for Theoretical Astrophysical Research.