I'll take a shot at this one as I'll be doing the exact same exercise for my work soon.
So the antenna impedance appears to be 60-j21 ohms:
And the impedance looking out into L3 is 31-j7 ohms:
(This would imply a source impedance of 31+j7 ohms).
So how can we get from 60-j21 to 31-j7 ohms? A two-element matching network can do it.
All that's necessary to make a match is two components. Here are a couple possibilities:
So the two two-component possibilities are high-pass (series L, parallel C) or low-pass (series C, parallel L). If the matching network is used as a filter for harmonic suppression, then the low-pass form is preferred.
On the other hand, the 24L01 outputs have a DC level at the power supply voltage. If you don't want DC on your antenna, a topology with a series capacitor for DC blocking may be desirable.
If the matching network is being used for filtering, it is desirable to be able to set the Q of this filter to get a steeper shape factor. Two topologies for this are the "PI match" and the "Tee match." Essentially they are two back to back two-element networks, matching to an intermediate impedance to set the desired Q.
(to be continued)
Without more information about your design I can't comment on the matching techniques. But here is some help for your test setup.
You can attempt to make relative measurements, but RSSI is a poor parameter for verification because you have to make sure you're in the linear range of the RSSI for the comparisons to be somewhat similar. Be aware that RSSI is just a current measurement of how saturated the amplifiers are and in general is not very accurate.
A spectrum analyzer would tell you much more and be able to give you a quick idea of how your device performs across the band.
Barring all that...you'll need to test this in an open area, outside, to avoid multipath interference. The more open and lacking of objects (especially metal), the better. Make two movable test stands (plastic or fiberglass is best) with batteries for power. Measure the distance between your reference receiver and your test transmitter (DUT).
Start with the manufacturers reference and characterize it at low/mid/high bands. Make sure your RSSI readings are stable and your background measurements (with no transmitter in operation) are quiet. The ISM900MHz band can be very noisey, so be careful of false readings using RSSI. You might find you're constantly turning on and off the transmitter to check background levels.
The RSSI needs to be in about the middle of it's range. If it is not, move the units closer or further apart. Measure this distance carefully so you can repeat it in the future...and don't loose your reference receiver! Also keep track of the orientations used and make sure the cables are carefully laid out, taped down for repeatability (both receiver and DUT). You might even want to lay down some copper screen material under the receiver and DUT to provide a more consistent ground plane for testing. Try to run the wires down through the center of the screen under the device.
Then take your design at the same distance and repeat the measurements across the band. With RSSI +/-3 dB is probably about all the accuracy you could expect. And since your design is physically different you might need to test a variety of orientations to insure you're getting consistent results and not testing at some antenna null or lobe.
Best Answer
First, before you can duplex any antenna, you have to find a way to keep the Tx signal from "blowing up" your Rx circuitry. The 2 most popular methods (that I'm aware of) are notch filtering (complicated & expensive, but allows full duplex) and switching (simpler & cheaper to impliment, but only half-duplex).
Using switching for illustrative purposes, you'll need a (preferrably solid-state) switching device that can disconnect the antenna from the Rx pin(s) when the device is actively transmitting (may possibly have already been done internally to your device).
You then simply attach both differential circuits (Tx & Rx) to the switching device; then attach the switching device to an impedance-matching balun; then attach your unbalance feedline (i.e. coax) or antenna to the other side of the balun.
This assumes you are A: Not using an external amplifier, and B: relying solely on your Tx/Rx chip for filtering (DC blocking simply requires coupling capacitors on the chip's Tx & Tx inputs; the balun can be used to ground any DC [static] charge building on the antenna).
Here is a writeup covering some basic balun design info (keep in mind that at 2.5GHz you WILL NOT need to use a "core"...a 5:1 impedance coil @ that frequemcy is quite small as an air-cored inductor!);
Then you can calculate the "turns ratio" for your impedances as: BalTurns/UnbalTurns = sqrt(BalOhms/UnbalOhms);
Then check out this inductive reactance calculator, and this inductor winding calculator to figure out what exact dimensions you need to use for your balun's coils (remember, you want to have 5x the reactance of your signal impedance on the coil to ensure good efficiency/transfer).