I want to use the MCP1501 precision voltage reference in an ADC circuit and have the issue that the reference produces a very noisy output. Much worse than an average LDO.
I have a VPP of 200mV when using the reference circuit shown in Figure 5-1 on page 19 of the Datasheet: http://ww1.microchip.com/downloads/en/DeviceDoc/20005474C.pdf
How can this happen? Does the output have to be connected to a load?
Here is the measurement on the scope: 
Answer
1st ensure you are not seeing capture measurement error across your decoupling cap near IC.
Probe ground and check you get a noise free flat line.
If not, arrange for 2 pins or short wires <1cm on Vref and gnd to be probed with tip and ground wire removed and use barrel ground to gnd pin and pin for signal to get the cleanest signal.
Convenient method below. 
Better method for SMD below.
You can buy these spring attachments for convenient accurate low noise measurements on 10:1 probes. ( or makeshift from pen spring ;)
Then ensure BW of scope is limited to range of spectrum expected. e.g. 10MHz here.
To locate EMI use the probe as a loop antenna then with gnd clip shorted to pin and wave over affected inductor current loop on SMPS to see what is being inductively coupled to high impedance tracks.
THen adding series choke or ferrite bead can raise track impedance >1MHz thus improve ZL/ZC LPF effects. Ensure Caps are low ESR.
Lastly ensure output cap value min/max and ESR min/max is added as recommended in datasheet.
ref: datasheet... Noise should be < 30nV per square root Bandwidth of signal captured or 6uV pp max with no load.
C load must be << 0.1uF for good phase margin if RL<1K.
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