Found in a comment by user @tspthomas.

keras_tensor_export.py

'''
I managed to export a Keras model for Tensorflow Serving (not sure whether it is the official way to do 
this). My first trial prior to creating my custom model was to use a trained model available on
Keras such as VGG19.
Here is how I did (I put in separate boxes to help understanding and because I use Jupyter :)):
'''

#Creating the model

import keras.backend as K
from keras.applications import VGG19
from keras.models import Model

# very important to do this as a first thing
K.set_learning_phase(0)
model = VGG19(include_top=True, weights='imagenet')

# The creation of a new model might be optional depending on the goal
config = model.get_config()
weights = model.get_weights()
new_model = Model.from_config(config)
new_model.set_weights(weights)
Exporting the model

from tensorflow.python.saved_model import builder as saved_model_builder
from tensorflow.python.saved_model import utils
from tensorflow.python.saved_model import tag_constants, signature_constants
from tensorflow.python.saved_model.signature_def_utils_impl import build_signature_def, predict_signature_def
from tensorflow.contrib.session_bundle import exporter
export_path = 'folder_to_export'
builder = saved_model_builder.SavedModelBuilder(export_path)

signature = predict_signature_def(inputs={'images': new_model.input},
                                  outputs={'scores': new_model.output})

with K.get_session() as sess:
    builder.add_meta_graph_and_variables(sess=sess,
                                         tags=[tag_constants.SERVING],
                                         signature_def_map={'predict': signature})
    builder.save()
'''
Some side notes:

It can vary depending on Keras, TensorFlow, and TensorFlow Serving version. I used the latest ones.
Beware of the names of the signatures, since they should be used in the client as well.
When creating the client, all preprocessing steps that are needed for the model (preprocess_input() for example) must be executed. I didn't try to add such step in the graph itself as Inception client example.
In case you're curious about the client side, it should be similar to the below one. I added some extra things to use Keras methods for decoding predictions, but it could also be done in the serving side:
'''

request = predict_pb2.PredictRequest()
request.model_spec.name = 'vgg19'
request.model_spec.signature_name = 'predict'
request.inputs['images'].CopyFrom(tf.contrib.util.make_tensor_proto(img))

result = stub.Predict(request, 10.0)  # 10 secs timeout
to_decode = np.expand_dims(result.outputs['outputs'].float_val, axis=0)
decoded = decode_predictions(to_decode, 5)
print(decoded)