The Basking Shark ( Cetorhinus maximus) is an elusive creature that possesses a highly-specialised filter-feeding system capable of filtering around two million litres of water every hour. Learning from such filters could be instrumental in making new filtration systems for microplastics or pollutants in the future. However, the specific filtration mechanism, as well as many other aspects of their morphology and behaviour, is not well understood. There are numerous difficulties involved with the study of basking sharks, particularly finding the sharks in their ocean habitat and observing them without disturbing them. Here, we propose a robotic platform, the System for underWater Imaging and Monitoring for Marine Environment Research (SWIMMER, SWIM for short), for the non-invasive imaging of basking sharks. The robot was designed to produce high-resolution stereo images at both surface level and underwater. The imaging payload is carried by a surface robot to make it easy to monitor, control, and retrieve. The robot is built low-cost and entirely from off-the-shelf components and 3D printing to enable us to scale up the robot to a swarm in the future for imaging from multiple points of view and for other marine applications. In a single trial, we were able to collect video data from 6 different basking shark encounters with 9 different individuals, as well as gathering data about manoeuvrability. This work has the potential to provide new insights into basking shark feeding behaviour, as well as potentially making marine swarm robotics more accessible to researchers everywhere due to the low cost and ease of construction of the SWIMMERs.