When I scroll further down the webpage, I notice that a sample document appears. There are no images in it, but coat of arms descriptions are written out in text. Let's see if the coat of arms of the Van Delft family is described in the document.
When I use the search function and type “Delft”, I get seven results. The first result is on page 553. Delft (from) is still just on this page. When I then scroll to the next page, the name immediately drops Jean-Baptiste-Joseph van Delft me up. This person matches the person on the Wikipedia page. In 1792, Empress Maria Theresa granted hereditary nobility to Jean-Baptiste-Joseph van Delft. This is also stated in the document:

Below is a description of the coat of arms. Unfortunately for me, it is unreadable because I've known since middle school that I definitely have no talent for the French language. But when I look further down the page, I see the following:

With the grandson Joseph-Gaspard van Delft, the coat of arms description is in Dutch. That helps! Or does it?
Coat of arms of silver, charged with a fess, and accompanied in chief by two open diamonds, all gules.
What does this actually say? I recognize some of the terms, but others I don’t. It turns out this is written in heraldic language. It contains all sorts of terms that mean nothing to me, but some elements are recognizable. When I do a quick search online, I come across a page with technical terms from heraldry. Let’s see if I can find anything about the unfamiliar words:
Strips = crossbar
Head Chef = placed in the shield's crest
Keel = red
So it actually says:
A shield of silver, charged with a crossbar, and accompanied in the chief by two open diamonds, all in red.

This matches the image on the portraits exactly. So we have proof that this is indeed a “Van Delft.” But which one? We’ll have to figure that out based on the lady’s family coat of arms. We have two names:
Nelly Baré en Delia Guyot
Let's start with the Baré family. As I go through the document, I come across Baré (the). I have no idea if this is the same family, but when I look at the coat of arms description, my heart sinks. I think this one is written entirely in Latin:
Coat of arms: An upright red military shield, displaying a gold chevron, accompanied at the base similarly by a gold spur or rowel.
I really can't make heads or tails of this. Even a crash course in Latin wouldn't help me.
Let's see if we can find anything about the Guyot family. I use the search function within the document again and get the following result:

Or, a lion gules, armed, langued, and crowned azure, with a chief of silver, charged with two griffin’s paws sable, clawed gules, and crossed in saltire.
This isn't just in French, but it also involves heraldic terms again. My French is about as good as my Latin. But let's see if the internet has a solution. And sure enough, after a long search, I end up on a page with a French description of the heraldic terms: Heraldic glossary
Let's see how far we get:
d’or = made of gold
a lion gules = with a red lion
armé armed
lampassé and crowned with azure = toothed and crowned in blue
with a silver-stitched cap = Silver sewn onto the upper shield
charged with two griffin's paws in sable = occupied by two black griffin pawns
gules with claws = Claws of Red
and worn as a long necklace = and arranged in a crisscross pattern
The description will then be as follows:
A gold shield bearing a red lion, armed, with a blue tongue and a crown, surmounted by a silver escutcheon set with the crossed forelegs of a black griffin with red claws.
Put simply: A coat of arms of gold with an armed red lion whose tongue and crown are blue. On the top of the shield are two crossed legs of a black griffin with red claws.

Suddenly I feel nauseous and lightheaded too. Have we really solved the mystery now? When I compare the description with the image of the weapon, I really clearly see similarities. It might not be very easy to see, but I am devoutly convinced that we now know exactly who the portrayed people are.
May I therefore introduce to you:

Alphonse van Delft (1817-1894) – Delia Guyot (1828-1898)

Alphonse van Delft 
Alphonse van Delft close-up 

I feel truly happy. After a lot of detective work, I can now truly say that we have found the portrait subjects. I now feel like I know them, even though only limited information is available. As I stare at the portraits, I try to imagine how these people stood posing for the painter. The painter? Who is this fantastic painter???………….

Alphonse Louis van Delft ° Antwerp 21-03-1817, baptized in St. James's Church on 01-04-1817, and died there on 14-08-1894. His godfather was Jozef Gaspard van Delft and his godmother was Isabelle Josèphe van der Aa de Randerode; He was dyke reeve of the Oosterweel polder and municipal councilor of Ekeren. Married in Antwerp on 11-05-1843 to Delia Isabella Guyot (de Mishaegen) ° Antwerp 24-05-1822 + Antwerp 23-12-1898.
Where can these portraits, which were unknown to me, be found?
Dear Mr. Van Delft,
Thank you very much for this wonderful addition. We are in possession of the portraits.
Is this related to you?