A new platform (sometimes referred to as a "caddy") for transporting a carpet cleaning machine includes a base for supporting the machine and a machine restraint mechanism for releasably coupling the machine and the platform to one another. The platform also has wheels (or an elongated roller-like wheel) mounted with respect to the base for rolling the base and the machine across a surface. The restraint mechanism has features preventing relative platform-machine movement along a single axis or, when the mechanism includes pairs of two different types of restraining members, along plural axes. A new method is used for transporting a carpet cleaning machine of the type having a carpet brushing apparatus and a brush drive motor. The method includes the steps of providing a transport platform having a base, energizing the brush drive motor and tipping the machine to transfer more weight onto a brush. Such weight transfer causes the apparatus to urge the machine onto the platform. The machine and the platform are then coupled to one another using one or more restraint mechanisms.