How to make two parallel convolutional neural networks in Keras?
You essentially need a multi-input model. This can only be done through keras' functional api and can work with the pretrained nets in keras.applications. To create one you can do this:

from keras.layers import Input, Conv2D, Dense, concatenate
from keras.models import Model


1) Define your first model:

 in1 = Input(...)  # input of the first model
 x = Conv2D(...)(in1)
 # rest of the model
 out1 = Dense(...)(x)  # output for the first model


2) Define your second model:

 in2 = Input(...)  # input of the first model
 x = Conv2D(...)(in2)
 # rest of the model
 out2 = Dense(...)(x)  # output for the first model


3) Merge the two models and conclude the network:

x = concatenate([out1, out2])  # merge the outputs of the two models
out = Dense(...)(x)  # final layer of the network


4) Create the Model:

model = Model(inputs=[in1, in2], outputs=[out])