The UT-61E can also test capacitance FYI, so you could definitely use it to measure the capacitance.
For best results, you'd need to test the capacitors out of the circuit (if you measure capacitors that are connected in parallel, you wont get an accurate reading). Set that aside though, in order to fully test a capacitor, you need to measure both the capacitance and ESR.
Your UNI-T can only measure the capacitance, which is better than nothing of course, but it wont tell you for 100% whether the capacitors are good or not (as in some cases, a capacitor can have good capacitance, but bad ESR levels, which will make it function poorly!)
You can get the MESR-100 (ESR meter) from a variety of places (such as fasttech/dealextreme/banggood, ebay or aliexpress sellers), it's reasonably affordable ($55) and provides a great value for money.