The current document is directed to methods and systems that generate recommendations for resource specifications used in virtual-machine-hosting requests. When distributed applications are submitted to distributed-computer-system-based hosting platforms for hosting, the hosting requester generally specifies the computational resources that will need to be provisioned for each virtual machine included in a set of virtual machines that correspond to the distributed application, such as the processor bandwidth, memory size, local and remote networking bandwidths, and data-storage capacity needed for supporting execution of each virtual machine. In many cases, the hosting platform reserves the specified computational resources and accordingly charges for them. However, in many cases, the specified computational resources significantly exceed the computational resources actually needed for hosting the distributed application. The currently disclosed methods and systems employ machine learning to provide accurate estimates of the computational resources for the VMs of a distributed application.