Portage Glacier and its lake were opened to kayaking in 2009 by the National Park Service. It's also close to Anchorage!
Floatation devices are a necessity: it's glacial water, super cold, and full of silt. This means swimming without dry suits is not an option, even in emergencies. Even in dry suits, silt can weigh material down. I've never tried it and don't intend to.
It's worth a stop into the Begich Boggs Visitors Center, named for two former Congressmen, to get directions and see the map of the zone they prefer kayakers stay inside of. This effectively runs along the Northeastern part of the shore, along the far side of the lake from the visitors center. This ensures kayakers will stay well enough from the glacier itself, where it is still calving. We could hear several booms and groans, even across the lake. (Trust me, you'll get plenty of chances to see ice bergs up close along the way.)
They can also show you where the kayak launch is.
The kayak launch is on the far side of the lake from the Begich Boggs Visitors Center, across the bridge and just through the tunnel. It is on the right with its own pull off and parking lot.
The boat launch is a narrow trail about 100-200 feet long from the parking lot on the right side of the road. The trail is near the far (East) side of the parking lot/pull out. Reminder: be bear aware and safe! (It is narrow and forested.)
If you had a folding kayak such as I did, it might be easier to assemble it in the parking lot and then carry it down, rather than assemble it on the narrow beach that the path opens onto. It's shallow enough to launch, but is also a little rocky.
When you're on the water, keep in mind the "williwaw" or Taku winds blowing off the glacier. Just like Lake Eklutna, there can be rapid changes. Today, even with a lot of sunlight and temperatures around 70 degrees, we faced a persistant headwind with some chop as we paddled towards the glacier. This wasn't too bad until we were 3/4 of the way there, when following the contours of the shore it puts your gunnell against the wave, rather than the bow. The kayak zone effectively keeps you close to the cliffs, with lots of waterfalls and sheer faces. With wind changes, this would be something to keep in mind.
For the most part, it was good but we had just enough headwind for us to make it a chore if we stopped to take a picture or grab the water bottle. It still only took us just about an hour. After just under 2.5 miles, you'll come to the destination!
The destination isn't the glacier, but the Southeastern corner of the lake, opposite the glacier, with uninterrupted views of the glacier(s) and waterfalls. There amazingly pleasant, expansive black sand beach, perfect for taking a break and hauling out. There's also lots of ice bergs that wash up on this shore as its directly opposite the glacier: very picturesque!
There's also trail that comes down to this beach from Whittier: so in case of emergency, it's a handy thing to know. Hikers told us it was a 2 hour hike to Whittier along a pretty well established trail. There is a signpost with map available. (This is where packrafters can also head on out up to or from Whittier. Keep in mind, we saw some rafters heading over from the boat launch and they had quite a bit of heaving with the waves and headwind.)
It was a beautiful and sunny paddle, and the headwind turned into a tail wind when we went back. We made it back in about 35 minutes, noticeably faster!
Drive one hour south (54.6 miles) along the Seward Highway, past Girdwood and Alyeska: there is a turnoff to Portage Glacier and Whittier clearly marked. Be warned: it is a left hand turn across traffic, which can be high on the Seward.
Follow the park road signs to the Begich Boggs Visitors Center, which is off to the right. They have facilities and a map available showing the kayaking zone that they prefer boaters stay inside of.