There’s a pretty cool app I’ve been using lately called CloudClip. It allows you to seamlessly sync your clipboard items between your iOS devices and your Mac via iCloud. Regardless of what you copy, your clipboard items will appear within the ClipBoard app on your iOS device and the ClipBoard app on your Mac.
The app syncs your items via iCloud and tracks your 15 most recent clipboard entries. Depending on what you copy, there are built in actions. For example, with URLs you can just tap to open in your browser (a choice of Safari or Chrome on iOS) and with phone numbers you can just tap to dial. Below are images of my quick tests with CloudClip. Once setup properly, my clipboard items just magically appear on both my iPhone and Mac:
Of course you could be using iCloud Tabs for syncing your open tabs within Safari and Mobile Safari (or sign into Chrome to sync tabs too). But CloudClip syncs your clipboard items beyond web URLs. Previously, I was using KeepItWith.Me to quickly send web URLs between my iPhone and Mac web browsers.