(Bump on an old thread). Just for kicks, here's a version that uses pointers to assemble the result string. It's about 2x - 4x as fast as the faster second version in the accepted answer.
Public Declare PtrSafe Sub Mem_Copy Lib "kernel32" _
Alias "RtlMoveMemory" (ByRef Destination As Any, ByRef Source As Any, ByVal Length As Long)
Public Declare PtrSafe Sub Mem_Read2 Lib "msvbvm60" _
Alias "GetMem2" (ByRef Source As Any, ByRef Destination As Any)
Public Function URLEncodePart(ByRef RawURL As String) As String
Dim pChar As LongPtr, iChar As Integer, i As Long
Dim strHex As String, pHex As LongPtr
Dim strOut As String, pOut As LongPtr
Dim pOutStart As LongPtr, pLo As LongPtr, pHi As LongPtr
Dim lngLength As Long
Dim cpyLength As Long
Dim iStart As Long
pChar = StrPtr(RawURL)
If pChar = 0 Then Exit Function
lngLength = Len(RawURL)
strOut = Space(lngLength * 3)
pOut = StrPtr(strOut)
pOutStart = pOut
strHex = "0123456789ABCDEF"
pHex = StrPtr(strHex)
iStart = 1
For i = 1 To lngLength
Mem_Read2 ByVal pChar, iChar
Select Case iChar
Case 97 To 122, 65 To 90, 48 To 57, 45, 46, 95, 126
' Ok
Case Else
If iStart < i Then
cpyLength = (i - iStart) * 2
Mem_Copy ByVal pOut, ByVal pChar - cpyLength, cpyLength
pOut = pOut + cpyLength
End If
pHi = pHex + ((iChar And &HF0) / 8)
pLo = pHex + 2 * (iChar And &HF)
Mem_Read2 37, ByVal pOut
Mem_Read2 ByVal pHi, ByVal pOut + 2
Mem_Read2 ByVal pLo, ByVal pOut + 4
pOut = pOut + 6
iStart = i + 1
End Select
pChar = pChar + 2
Next
If iStart <= lngLength Then
cpyLength = (lngLength - iStart + 1) * 2
Mem_Copy ByVal pOut, ByVal pChar - cpyLength, cpyLength
pOut = pOut + cpyLength
End If
URLEncodePart = Left$(strOut, (pOut - pOutStart) / 2)
End Function