The RSA300API.DLL might have dependencies in the folder so prior to using it, use os.chdir to set the working directory, for example:

import os

os.chdir(r'C:\Tektronix\RSA306 API\lib\x64')
rsa300 = ctypes.WinDLL(r"C:\Tektronix\RSA306 API\lib\x64\RSA300API.dll")

Checking one of their samples, this appears to be the recommended way to access it.

Alternatively, as @eryksub has mentioned, LoadLibraryEx can be used. win32api could be used to get the handle and pass it to WinDLL as follows:

import ctypes
import win32api
import win32con

dll_name = r'C:\Tektronix\RSA306 API\lib\x64\RSA300API.dll'
dll_handle = win32api.LoadLibraryEx(dll_name, 0, win32con.LOAD_WITH_ALTERED_SEARCH_PATH)
rsa300 = ctypes.WinDLL(dll_name, handle=dll_handle)

I think your problem might be here:

mecab_dll = ctypes.WinDLL(r"C:\libmecab.dll")

WinDLL means use Windows DLL calling convention (stdcall). However, in C#, you're using C calling convention (cdecl):

[DllImport(@"C:\libmecab.dll", CallingConvention = CallingConvention.Cdecl, CharSet = CharSet.Unicode)]

If your C# code works, try re-writing your ctypes call like this:

mecab_dll = ctypes.cdll.LoadLibrary(r"C:\libmecab.dll")

Edit: You're also doing quite a bit of work to pass that string to your function. You should be able to simply do this (I'm not 100% certain this will work in Python3 - it works flawlessly in Python2):

mecab_dll = ctypes.cdll(r"C:\libmecab.dll")
res = mcab_dll.mecab_new2(b"-Owakati")

Python is quite intelligent about determining types in foreign functions - you shouldn't have to declare them unless you're doing something uncommon.

Edit 2 This works for me, using Python 2, 32bit: I'm doing this from an interactive prompt. Working directory is C:\Program Files (x86)\MeCab\bin

mecab = ctypes.cdll.LoadLibrary("libmecab.dll")
res = mecab.mecab_new2("-Owakati")

res is then a non-zero integer (appears to be a valid pointer).

You've tagged the question ctypes and so it sounds like you already know the answer.

The ctypes tutorial is excellent. Once you've read and understood that you'll be able to do it easily.

For example:

>>> from ctypes import *
>>> windll.kernel32.GetModuleHandleW(0)
486539264

And an example from my own code:

lib = ctypes.WinDLL('mylibrary.dll')
#lib = ctypes.WinDLL('full/path/to/mylibrary.dll')
func = lib['myFunc']#my func is double myFunc(double);
func.restype = ctypes.c_double
value = func(ctypes.c_double(42.0))

It appears you cannot just import ctypes.windll, you need to import ctypes and then use ctypes.windll. I discovered that by printing all properties of ctypes:

import ctypes
print dir(ctypes)

What's also interesting is that IPython autocompletion was misleading here, because it didn't show windll as a possible choice when TAB-autocompleting after import ctypes..