Continue For loop

You can use a GoTo:

Do

    '... do stuff your loop will be doing

    ' skip to the end of the loop if necessary:
    If <condition-to-go-to-next-iteration> Then GoTo ContinueLoop 

    '... do other stuff if the condition is not met

ContinueLoop:
Loop

For i=1 To 10
    Do 
        'Do everything in here and

        If I_Dont_Want_Finish_This_Loop Then
            Exit Do
        End If 

        'Of course, if I do want to finish it,
        'I put more stuff here, and then...

    Loop While False 'quit after one loop
Next i

You're thinking of a continue statement like Java's or Python's, but VBA has no such native statement, and you can't use VBA's Next like that.

You could achieve something like what you're trying to do using a GoTo statement instead, but really, GoTo should be reserved for cases where the alternatives are contrived and impractical.

In your case with a single "continue" condition, there's a really simple, clean, and readable alternative:

    If Not InStr(sname, "Configuration item") Then
        '// other code to copy paste and do various stuff
    End If

A lot of years after... I like this one:

For x = LBound(arr) To UBound(arr): Do

    sname = arr(x)  
    If instr(sname, "Configuration item") Then Exit Do 

    '// other code to copy past and do various stuff

Loop While False: Next x