The fittings for these bulbs will be the same as E27 and E14 etc. are standardized sizes across the board for all lighting technologies.  You may however find that there are differences between the length of the bulbs and the width of the glass body of the bulb.  It is worth double checking this when you are looking to purchase a replacement bulb.

Key Factors and Considerations

1. Base Cap Type

The most critical dimension for fit is the lamp base (cap). LED and CFL candle bulbs are manufactured with the same standard base types used for incandescent candle bulbs, such as E14, E27 and B15.  You can sometimes get caps outside of this such as E10 and B22 but these are less common.  All you will have to do for the cap measurement is make sure that the descriptor for it is the same as your previous bulb.

2. Bulb Shape and Dimensions

The main difference lies in the main body of the bulb.  The majority of LED and CFL lamps will be close to their halogen or incandescent counterparts but may be slightly longer in length or width due to the extra internal components needed for LED lamps.  As this can affect how they appear in your fitting or shade it is also worth checking the sizes listed on the replacement LED or CFL bulb you are looking to purchase.

Summary of what to do when looking for a replacement that is LED/CFL:

1. Check the Base: Confirm the base type and look for a number that looks like E14 or E12.
2. Measure the Old Bulb: Make a note of the diameter and the overall length of the incandescent/halogen bulb you are replacing.  You should also consider if you can have a bulb that is larger or longer depending on the fitting as this may affect how it looks once fitted.
3. Look for a bulb that has the same finish: If appearance is key for your bulbs you should make sure the replacement bulb has the same finish.  This will be listed in the description of the bulb such as clear or frosted.