Testing for mandatory parameters with Pester

Per the comments from Mathias, you can't really test for whether a Mandatory parameter is missing because PowerShell prompts for it rather than throwing an error. Per the comment he linked to from the Pester team you could use Get-Command to test for the Mandatory parameter setting in the script (assuming it is the only parameter attribute set for that variable)

((Get-Command "$here\$sut").Parameters['ComputerName'].Attributes.Mandatory | Should Be $true

An alternative option would be to not use Mandatory parameters in this instance, and instead have a script block that does a Throw as the default value of the parameter:

Param (
    [String]$ComputerName = $(Throw '-ComputerName is required'),
    [String]$ScriptName
)

If the script is always used as part of an automated process (instead of via user execution) this might be preferred as it allows you to control/capture its behavior and avoids it getting stuck during execution. You can then test the script as you had originally proposed:

Describe 'Mandatory paramters' {
    it  'ComputerName' {
        {
            $Params = @{
                #ComputerName = 'MyPc'
                ScriptName   = 'Test'
            }
            . "$here\$sut" @Params
        } | Should throw '-ComputerName is required'
    }
}