Ok, so I've made further research, and I finally found something that's working, using cURL. In order to make it, we have to make a function like this (this is a function I found here VBA Shell function in Office 2011 for Mac) :
Private Declare Function popen Lib "libc.dylib" (ByVal command As String, ByVal mode As String) As Long
Private Declare Function pclose Lib "libc.dylib" (ByVal file As Long) As Long
Private Declare Function fread Lib "libc.dylib" (ByVal outStr As String, ByVal size As Long, ByVal items As Long, ByVal stream As Long) As Long
Private Declare Function feof Lib "libc.dylib" (ByVal file As Long) As Long
Function execShell(command As String, Optional ByRef exitCode As Long) As String
Dim file As Long
file = popen(command, "r")
If file = 0 Then
Exit Function
End If
While feof(file) = 0
Dim chunk As String
Dim read As Long
chunk = Space(50)
read = fread(chunk, 1, Len(chunk) - 1, file)
If read > 0 Then
chunk = Left$(chunk, read)
execShell = execShell & chunk
End If
Wend
exitCode = pclose(file)
End Function
Basically, this function allows us to call shell commands on Mac, without having to go through all the struggle of converting Mac commands to Windows format.
Once this is done, call this function with the first parameter being the command line (in cURL format), and the second a reference to the exit code returned by the system (and not the cURL request!). The cURL command will then return the http response. So something like this will work :
Dim command As String
command = "usr/bin/curl http://www.myserver.com -d "data" -X POST ..."
Dim exitCode As Long
Dim result As String
result = execShell(command, exitCode)
Notice how I'm starting my cURL request. You HAVE to write the path to cURL (in this case "usr/bin/curl") in order for the system to find cURL's location, otherwise it won't work (it may work, but this way we make sure it will always work)
Cross-platform compatibility
Please note that this solution however won't work if it's on windows, as it doesn't have "libc.dylib" librairies, so you'll have to check the Operating system and implement a way to do it on Windows (as written in the question)
Set objHttp = CreateObject("MSXML2.ServerXMLHTTP")
objHttp.SetOption 2, objHttp.GetOption(2) - SXH_SERVER_CERT_IGNORE_ALL_SERVER_ERRORS
objHttp.Open "POST", myURL, False
objHttp.SetRequestHeader "User-Agent", "Mozilla/4.0 (compatible; MSIE 6.0; Windows NT 5.0)"
objHttp.SetRequestHeader "Content-type", "application/x-www-form-urlencoded"
objHttp.SetRequestHeader "Authorization", "Basic " & Base64Encode(Username & ":" & Password)
objHttp.Send (strOutput)